The Toffees’ four-match unbeaten run on the road looked set to end thanks to Vitalii Mykolenko’s unfortunate 18th-minute own goal following a fine initial save by Jordan Pickford.

It would have made ugly viewing for David Moyes, up in the stands due to a touchline ban, but he watched Kiernan Dewsbury-Hall level with 15 minutes left before a corner by the same player was punched into his own net by Fulham goalkeeper Bernd Leno to consign Marco Silva’s men to a rare home defeat.

Moyes would have had the perfect vantage point for an Everton opener in the early stages, only for Jake O’Brien’s eighth-minute header to smash off the woodwork moments after James Garner had been denied from a free-kick.

Fulham regrouped and Pickford produced a wonderful save to deny Raul Jimenez before O’Brien cleared Sander Berge’s follow-up effort.

O’Brien was required to intercept another dangerous cross soon after before Fulham broke the deadlock in the 18th minute in fortuitous circumstances.

Samuel Chukwueze chipped the ball into the path of Alex Iwobi, who was tackled inside the area, but Ryan Sessegnon found Jimenez and, even though Pickford produced a wonderful stop to deny the Mexican, the loose ball hit team-mate Mykolenko and bounced in.

Pickford, under the watchful eye of England head coach Thomas Tuchel, was furious but had little time to dwell on the goal, with Chukwueze the next to test the Everton keeper.

All the momentum was with Fulham now and, after Emile Smith Rowe struck the crossbar with a brilliant curled effort, Jimenez should have made it 2-0 in the 31st minute but dragged his effort wide after more fine play down the hosts’ left.

It largely remained one-way traffic, with Harry Wilson the next to fire off target when he uncharacteristically snatched at a chance before Pickford rushed out to deny Smith Rowe from another excellent Chukwueze pass.

Chukwueze almost grabbed a deserved goal before the break, but his 30-yard piledriver clipped the crossbar.

Everton returned for the second half with improved intent and Thierno Barry headed wide from a corner.

Fulham arguably should have put the game to bed just past the hour mark when Wilson played in Chukwueze, who squared for Jimenez, but O’Brien did enough to deny the forward from close range.

James Tarkowski sent a header off target moments later as anxiety increased around Craven Cottage.

Moyes reacted with Beto and deadline-day arrival Tyrique George introduced and six minutes later Everton levelled.

Mykolenko atoned for his own goal with a fine burst beyond Joachim Andersen before his pull-back was swept home by Dewsbury-Hall.

Leno may have done better and, although he denied Beto soon after, the Fulham keeper was at fault for Everton’s 83rd-minute winner.

Dewsbury-Hall sent his corner to the near post, where O’Brien made a nuisance of himself and Leno could only punch the ball weakly into his own net.

Seven minutes were added on, but Everton held on as Moyes celebrated more away-day success.