Dominic Calvert-Lewin wrote another chapter in his breathtaking start to this season with a hat-trick as Everton won their sixth straight game from the start of a campaign for the first time in 82 years.
This wasn’t as straight forward for Everton as the scoreline suggests.
Indeed the Blues were at their most fluent before half-time and were unlucky to lead only 1-0 at the interval.
Robert Snodgrass equalised immediately after the restart – which angered Everton.
They’ve been here before of late, pegged back by both West Bromwich Albion and Crystal Palace before running out winners.
Everton promptly hammered on West Ham’s door and crashed through when Richarlison meandered across the edge of the box before unleashing a drive which deflected off Declan Rice and wrong-footed Darren Randolph.
Richarlison was soon forced off injured, however and Everton will be keeping their fingers crossed following problems for three players.
The brilliant pair of Richarlison and Allan went off inside eight hurtful second-half minutes – after Jonjoe Kenny’s enforced withdrawal four minutes before the break.
It was Richarlison’s replacement Alex Iwobi who did a lot of the leg work for Everton’s third goal.
Collecting a pass from Gylfi Sigurdsson, he crafted room to shoot, striking the far post.
The ball rebounded for Calvert-Lewin to turn home.
And when Calvert-Lewin completed his second treble in 11 days, Everton were guaranteed their Carabao Cup fourth-round place.
Sigurdsson was the provider, forcing a pass through a narrow gap. Calvert-Lewin prodded past Randolph for his eighth goal of the campaign.
From Michael Keane’s carefully lifted pass from his own half, through Calvert-Lewin’s gorgeous touch to pull the ball from the sky, to the striker’s classy finish, Everton’s first goal was a work of art.
Calvert-Lewin left Declan Rice trailing to fasten onto the pass from Keane, who skilfully avoided a challenge from Manuel Lanzini before releasing his teammate.
The Everton forward used his left instep to control, steadying himself before easing his right-footed finish past Randolph.
Carlo Ancelotti’s teamsheet read like a statement of intent, James Rodriguez and Allan both included for their first Carabao Cup appearances.
And James was in sumptuous touch, gliding between wings to feed a succession of wonderful passes to his forwards.
One ball inside Ben Johnson for Richarlison defied science and drew audible gasps from those fortunate enough to be inside Goodison Park.
Richarlison gave it the finish it deserved, too, but the Brazilian had strayed marginally offside before placing the ball in the net.
James was having fun running with the ball, his opponents backing off every time.
Snodgrass got in a tangle and ended up on the deck trying to halt the Colombian in one instance.
When James went deeper, he fed a ball down the line for Calvert-Lewin – repeatedly running down young right-back Johnson’s channel.
Calvert-Lewin cut inside but sent his strike from 18 yards whizzing over the top.
For all the magical moments from James and Richarlison, it was Everton’s third South American in Allan who drew an appreciative roar from his watching teammates with a terrific challenge to thwart Felipe Anderson on the break.
Anderson had forced Jordan Pickford into a save down to his right on seven minutes but there was little from West Ham going forwards.
Lanzini tumbled in the box but was penalised for handball and Sebastien Haller couldn’t stretch far enough to meet a terrific Aaron Creswell delivery from the left.
Another Creswell cross, moments before half-time, was headed beyond the far post by Lanzini.
The visitors were unsure at the back, Creswell keeping Randolph honest with a hard-hit backpass and Fabian Balbuena heaving a sigh of relief when his gift of possession to Calvert-Lewin came to nothing.
West Ham’s hesitancy was understandable nevertheless. If it wasn’t James gunning for them, it was Richarlison.
Scorer of three goals in his past two games – including a double in the previous round at Fleetwood Town – Richarlison began here with a surge into the box which required three defenders to stop.
He danced through again on 20 minutes, slipping inside Balbuena and opting to shoot early with the outside of his left boot.
Randolph did very well to scoop the ball over at close range.
The one disappointment for Everton in the opening 45 minutes came with the injury to Kenny, who insisted on staying on the pitch to avoid leaving his team a man short defending a corner before hobbling off.
The home team sustained another blow scarcely 20 seconds after the restart.
West Ham’s equaliser was simple in its execution but an excellent strike from Snodgrass.
Anderson collected an overhit cross on the left and fed the ball back for Snodgrass on the edge of the box.
The Scot met it first time with a shot which arced across Pickford and into the right corner.
Everton responded with a Richarlison strike from the left of the box against the base of Randolph’s right-post and a shot from distance hit too high by Calvert-Lewin.
Allan was brilliant again to scupper Anderson on the counter, then it was James and Richarlison back to the fore, combining to supply Gylfi Sigurdsson in the middle of the penalty area.
Sigurdsson’s shot was firm but repelled by the excellent Randolph.
The goalkeeper was stranded soon after, though, Randolph initially shifting left when Richarlison let fly from 18 yards – but undone by a deflection off Rice’s back which sent the ball on a trajectory down the middle of goal.
Richarlison’s night was ended when he fell awkwardly, the South American replaced by Alex Iwobi.
The nature of these games, winner-takes-all and no extra-time meant West Ham would inevitably begin throwing caution to the wind.
A cluster of claret-and-blue shirts were waiting when Andriy Yarmolneko headed into the middle after Snodgrass dug out a cross.
The ball dropped for Lanzini but he dragged his effort wide.
Pickford athletically helped over an effort from Haller after the Frenchman controlled on his chest and aimed an overhead kick.
With Richarlison and Allan off, it appeared Everton were set for a backs-to-the wall job to see this out.
The red-hot Calvert-Lewin emphatically dismissed that notion.
Everton have scored 12 times in three games in this competition with a +9 goal difference.
Safe to say, their quarter-final berth is merited.
Everton’s manager will forgive Dominic Calvert-Lewin this one.
The striker has been prolific this term following Carlo Ancelotti’s advice to shoot with his first touch.
Calvert-Lewin used that method for four of his five Premier League goals.
But in much the same way his overall game has evolved over the past 12 months, the 23-year-old is capable of conjuring a variety of finishes.
He had been the focus of Everton’s attacking play before netting his eighth League Cup goal.
Calvert-Lewin began the game running behind West Ham right-back Ben Johnson, stretching West Ham before drilling a pass 20 yards back the way for Allan.
He had been strong with his back to goal, centre-half Declan Rice noticeably trying to smother Calvert-Lewin.
The Everton player evaded his man on 11 minutes, however – straight after Michael Keane had done likewise to Manuel Lanzini.
Keane, the only Everton player to begin all six games this term, pirouetted away from Lanzini, buying the time to have a look at the picture in front of him.
Seeing Calvert-Lewin escaping Rice, Keane sent a precise ball over the top for the forward to cushion quite brilliantly on his left instep.
If touch one was immaculate, the second didn’t suffer by comparison.
Calvert-Lewin deftly lifted the ball over keeper Darren Randolph for his sixth goal of the campaign.
Following close-range finishes for his hat-trick against West Bromwich Albion and again at Crystal Palace, and the rocket header which downed Tottenham Hotspur, here was further evidence of Calvert-Lewin’s growing arsenal.
When Alex Iwobi’s effort came off the post with 12 minutes remaining, Calvert-Lewin needed only one touch.
He wasn't done for the night either. Calvert-Lewin is never satisfied and when Gylfi Sigurdsson alighted on possession the striker made a clever run before adding a decisive touch.
He has 10 League Cup goals from seven starts in the competition.
Impressive in any context – but overshadowed by his eight goals from five starts this season.
Seemingly in the blink of an eye Everton are Carabao Cup quarter-finalists.
The logistics of this campaign demanded teams play three midweeks on the spin to reach the last eight.
Rather than view this arrangement as a bind, Everton saw an opportunity and pounced on it.
The challenges grew more complex by the round, this victory over Premier League rivals West Ham United following wins against Salford City of League Two and the League One side Fleetwood Town.
Everton saw off their lower division opponents with the minimum of fuss which is a skill in itself.
Every Evertonian can tell a tale of seeing their team toppled by an underdog and the same is true of supporters of all elite clubs. The Manchester City side which stacked up 100 Premier League points and won this competition in 2017/18 tumbled out of the FA Cup to Wigan Athletic.
In this respect Everton have been getting to grips with the League Cup the past few seasons.
Caretaker bosses David Unsworth and Duncan Ferguson could rightly rue their misfortune in the tournament.
Unsworth’s team lost a tight game at Chelsea three years ago.
Ferguson, last season, saw his team go out in the quarter-finals, beaten on penalties after recovering a two-goal deficit to draw with Leicester City.
Squeezed between those two near-misses was a penalty-shootout defeat to Southampton in 2018/19.
Everton came into this game on a high but so did their opponents after stunning Wolverhampton Wanderers 4-0 at the weekend.
West Ham were similarly ruthless in earlier rounds, breezing past the League One pair of Charlton Athletic and Hull City.
This was a tricky task, then, but one Everton and their manager met head on.
Ancelotti has progressively reduced his changes for these games – 10 against Salford, six for the trip to Fleetwood and four here.
Results judge the acuity of those tweaks and, evidently, Ancelotti has measured this cup run perfectly.
There was a lot on the line tonight. Had Everton gone out the early season optimism generated by a flawless five-game run would have been checked.
Progress and Everton could enjoy having this up their sleeves, channelling their energy into league matters knowing a big December cup tie is in the bank.
They didn’t have it all their own way, as was the case when Fleetwood rallied seven days ago.
But West Ham’s equaliser provoked Everton. The Blues created a rush of openings before Richarlison restored their advantage and Everton killed the game off with two late goals.
Ancelotti makes plain he wants Everton to make a very good fist of every competition.
With this success against West Ham they couldn’t be doing any more.
Niels Steps Up
Carlo Ancelotti said he would discover more about Niels Nkounkou tonight.
The 19-year-old full-back had a field day against the supposed lesser lights of Salford City and Fleetwood Town on his first two Everton appearances.
Matched against Premier League opponents this was a step up for Nkounkou – his first experience of facing top-flight opposition of any sort.
In Andriy Yarmolenko, Nkounkou had a vastly-experienced opponent, boasting 88 caps for his country and a lot of top-level European football with former club Dynamo Kiev.
And in denying Yarmolenko space, snapping into tackles and ushering the 30-year-old away from danger areas, Nkounkou showed defensive nous.
We didn’t see so much of the bombing on that was a hallmark of Nkounkou’s past two displays.
He selected his moments to overlap and held his position when the opposite full-back was upfield.
Nkounkou was accomplished in possession and passed the ball accurately in tight spaces relished his opportunity to crunch into a tackle on Ben Johnson at 2-1.
There was a school of thought suggesting Everton might look to supplement their full-back resources, certainly following the retirement of Leighton Baines.
Nkounkou, though, looks a viable option at left-back.
Additionally, everything we’ve seen from Jonjoe Kenny following his loan with Schalke 04 has been promising.
Kenny was very good again and suffered his injury executing a strong piece of defending tp stop Felipe Anderson crossing.
Full marks for character, too, Kenny refusing to leave the field until his team had defended the subsequent corner.