There was a period at the London Stadium when it appeared Everton would travel north with one point, minimum.

It wasn’t only the sight of the visitors drawing level courtesy of Mason Holgate’s strike eight minutes after half-time that prompted optimism.

Frank Lampard’s side played with energy and ambition and hunger and looked anything other than a team fighting to preserve its Premier League status.

The noise in the ground sparked by Aaron Cresswell’s free-kick opener for the hosts had been replaced by a concerned murmur rolling around the place. And, in the shape of Alex Iwobi and Richarlison and Demarai Gray, Everton boasted the game’s creative sparks.

But we are often told the margins in England’s top-flight are extraordinarily slender – and here, we had further proof of the veracity of that statement.

One lapse in midfield when Everton were in control – in that moment and in the match – led to Michail Antonio bearing down on the visitors’ goal.

Jordan Pickford, fresh from reminding the rest of the country what Everotnians already knew – he’s really rather good – saved from the striker. Jarrod Bowen, however, was following up to restore West Ham’s advantage.

This time, it was decisive. Everton’s push for a second equaliser took a serious hit when Michael Keane was sent off after collecting a second booking for a 65th-minute foul on Antonio.

Perhaps we should have known it wasn’t going to be Everton’s day when Donny van de Beek was hurt in the warm-up.

But when battlefield promotion Holgate smacked an equaliser with the aid of a deflection the headlines were being redrawn. The goal was no less than Everton deserved following a strong reaction to Cresswell’s opener - but ultimately not enough to earn a tangible reward for a predominantly positive display.

Everton passed the ball with speed and purpose in the opening half, seeking to move West Ham’s central defensive pillars out of position.

And the plan worked to an extent, Everton stretching the hosts and causing a degree of discomfort among a backline that tends to be fairly miserly at this cavernous stadium.

The visitors dipped into the route-one playbook for their clearest opening of the first half, nonetheless.

Ryan Fredericks, the West Ham right-back, misjudged a raking Pickford punt.

Richarlison spied Fredericks deliberating over whether to stick or twist and getting caught betwixt and between.

The Brazilian was away on his toes, then, when the ball made its way to his feet. Richarlison bustled into the penalty box, opting for a version of a banana shot with the outside of his right boot and lousy on himself when the ball travelled fractionally too high to bother Lukasz Fabianski.

Iwobi was the architect of a terrific chance five minutes after the restart. The Londoner strode through midfield and slid a pass down the side of Craig Dawson. Dominic Calvert-Lewin gathered but the rising drive cracked the frame of the goal on its way behind.

Everton were searching for an equaliser at this stage after falling behind to a goal that had its roots in an innocuous attack.

Holgate impeded Bowen 25 yards from goal.

Cresswell’s free-kick scooted over the five-man wall and rushed inside the post, defeating Pickford high to the keeper’s left.

Pickford had a mixed workload prior to the set-piece strike. A catch from a Bowen shy at goal qualified as very straight forward for the England man.

The same was probably true of a fabulous one-on-one save from Pablo Fornals – but only in the context of Pickford’s expertise in these situations.

Fornals’ eyes widened as Said Benrahma transferred Bowen’s pass to the Spaniard at the back post.

The ball was barely under control, however, than Pickford was narrowing the angle and saving with his legs.

Keane twice shielded Pickford in the opening 10 minutes.

Fornals was on target after a cut back from Fredericks but thwarted by Keane’s block.

And the ball spun behind off the defender following Antonio’s run into the box and low shot.

Everton were playing with intensity off the ball and rapid and direct on it.

Gray showed terrific intent, driving Everton forwards with his ability to carry the ball and eliminate opponents from the game.

Abdoulaye Doucoure snapped into tackles at both ends of the pitch. Iwobi, meanwhile, was a blend of both men, active out of possession and always minded to find a killer pass in the final third.

Confidence is a commodity routinely discussed around Everton right now.

There appeared no issue on that score whatsoever during a bright and progressive opening.

Kurt Zouma grew to his fullest height to stop Iwobi’s chipped ball connecting with Calvert=-Lewin.

Moments earlier, Calvert-Lewin, starting for the first time in four matches, arrowed a pass out to Jonjoe Kenny.

Richarlison attempted an overhead kick from the cross but saw the effort clatter into Dawson.

Everton’s football was fluid and imaginative and even when Richarlison’s ball into the box was too big, it was kept alive at the back post, Holgate fed for a firm strike – a precursor for his subsequent effort – that hit a defensive body.

Iwobi fashioned an opening for Richarlison on 29 minutes. Richarlison’s movement off his flank caught Fredericks off guard and the ball into the South American’s run was perfectly measured.

Fabianski was deceived by Richarlison’s first touch but with the forward seemingly poised for a shot at an open goal, Fredericks recovered to intervene.

Antonio lashed into the side netting after taking a long route around Pickford and the keeper’s reflexes were sharp when Kenny diverted Benrahma’s cross on target.

Everton’s equaliser was a reward for persistence and ambition.

Fabianski’s punch on Gray’s left-wing corner was okay, no more, leaving a bouncing ball up for grabs.

Richarlison used his strength to resist challenges and nudge it back for Holgate, who got his knee over the ball for a fierce attempt that flicked off Fornals and utterly defeated goalkeeper Fabianski.

Two tiers of Evertonians celebrated like mad and so did the away players in front of them.

Everton appeared to have gained the ascendancy only for a rotten seven minutes to swing momentum in the hosts’ favour.

Iwobi, otherwise immaculate, was unfortunate that his only loose touch of the game ran favourably for Benrahma, who promptly sprung Antonio.

He scampered into the box for a strike saved at close quarters by Pickford. The rebound ran for Bowen who easily converted.

Everton twice asked for penalties – for Richarlison and Holgate – but both appeals met the same deaf ears. The claim from Richarlison looked especially valid.

Keane collected his second booking for the same reason he picked up the first – a foul on Antonio – compelling Lampard to change tack again.

West Ham resisted the temptation of going for the jugular. Instead, the home team were content to try to manage the closing stages and reserve their offensive intent for counter-attacking opportunities.

Benrahma bobbled an effort wide shortly before Lampard replaced Calvert-Lewin with Anthony Gordon.

Everton prodded and probed but couldn't locate the decisive final ball. Pickford joined the attack for a free-kick in the last knockings of stoppage time but Gray's delivery sped to the back post where it was headed off target to ensure all three points stayed in the capital.