Everton were forced to settle for a point after an action-packed encounter at Fulham somehow ended goalless.
Strong claims for an Everton penalty were waved away midway through the first half after the ball struck former Blues youngster Antonee Robinson on the hand, before Arnaut Danjuma spurned an excellent chance after an impressive solo run.
Dominic Calvert-Lewin struck the crossbar with a headed effort early in the second half but Marco Silva's side dominated large parts of the second period, hitting the woodwork themselves through Timothy Castagne's header.
Ben Godfrey produced a superb passage of recovery defending to deny Willian, while Jordan Pickford pulled off an excellent save to keep out another headed effort from Tosin.
But Everton weathered the storm and almost pinched all three points in second-half stoppage time, as Beto headed over from two-yards out before Godfrey's late effort caused a goal-line scramble in the dying seconds.
Sean Dyche made four changes from the side that started the FA Cup clash with Luton Town, with Jordan Pickford, Godfrey, Ashley Young and Danjuma recalled to the starting line-up.
Amadou Onana missed out on the matchday squad, having sustained a minor knee injury at the weekend, meaning Dwight McNeil was deployed in an unfamiliar central role alongside James Garner.
London had been a happy hunting ground for the Blues so far this season, having already racked up wins in the capital over Brentford, West Ham and Crystal Palace this term.
Dyche's men started confidently here, too. The returning Young and Godfrey combining well down the right flank inside the opening two minutes before Jack Harrison curled his left-footed shot wide of the post after strong hold-up play by Dominic Calvert-Lewin, who may have been in an offside position.
Less than two minutes later, Everton were on the attack again. Mykolenko's low cross from the left was met by Calvert-Lewin but Tosin was on hand with a timely intervention to block the striker's effort.
Silva's men then forced Pickford into his first save of the night but England's No.1 carefully tracked Antonee Robinson's deflected shot from the edge of the penalty area to turn it behind for a corner.
The biggest talking point of an eventful opening period came at its halfway point.
Young used every ounce of his vast experience to bring down a high ball and draw foul from Robinson on the corner of penalty area. The 38-year-old then brushed himself down to take the result free-kick, forcing Bernd Leno to parry it back into the danger area, where James Tarkowski scuffed an effort towards goal. Issa Drop flicked it upwards with a header and as the ball brushed the crossbar on the way down, it struck Robinson on the hand as it trickled back towards the goal line, only for Timothy Castagne to stab clear.
Everton's players - and the 2,701 travelling away supporters behind the goal - appealed for a penalty, but referee Thomas Bramhall called for play to continue.
Despite trailing in the possession count, the Toffees continued to look the more dangerous outfit in attack.
The most presentable opportunity of the first half was made and squandered by Arnaut Danjuma.
After an excellent block by Vitalii Mykolenko to deny Bobby De Cordova-Reid's drive, Everton countered with purpose and, after scooping a deflected pass into his path on the halfway line, Danjuma bore down on goal and cut back on to his right foot but then blazed his right-footed effort over the target.
The hosts responded with a chance of their own, even if it came in particularly fortuitous circumstances.
De Cordova-Reid's speculative shot from the edge of the penalty was half blocked by Mykolenko and then hacked away from goal by Tarkowski. The rebound fell kindly for Raul Jimenez, but the Mexican drilled his shot well wide of the post.
The crossbar denied Everton 10 minutes into the second half when James Garner's deep cross from a corner was met by the head of Calvert-Lewin.
Then, just before the hour mark, Dyche's side were dealt a scare, as Branthwaite's attempted pass was charged down by De Cordova-Reid, springing a two-versus-one situation. Tarkowski did excellently to delay the Jamaican forward but Willian looked destined to score when he was eventually picked out, only for Godfrey to take the ball off his toe with a superb sliding challenge after an extraordinary burst of pace.
That chance triggered a frantic spell, with the Cottagers establishing themselves as the team firmly in the ascendancy.
Castagne headed against the crossbar from Pereira's corner, then Pickford produced an excellent diving save to claw Tosin's header behind minutes later.
But Dyche's battled through that testing period to find a foothold in the contest as it entered the closing stages.
The Toffees were dealt another injury worry as the clock struck 90 minutes, with Danjuma limping off with the help of the Club's physiotherapists.
There was time for three more huge moments in the six minutes of second-half stoppage time.
First, Fulham failed to take their chance to win it as half-time substitute Rodrigo Muniz diverted his free header straight at Pickford.
Then, at the other end, McNeil's deep corner was headed back across goal by Tarkowski and then over the target by Beto from two-yards out.
Another corner followed at the death, with Garner's delivery causing chaos inside the six-yard box and substitute Godfrey's effort hitting Beto before being squeezed away.
That was the final chapter of an incident-filled story on the banks of the River Thames.
Next up for Everton is the visit of Tottenham Hotspur at Goodison Park on Saturday (12.30pm GMT).