Everton scored two goals in three minutes to hurt Fulham’s European qualification hopes with a 3-1 win at Craven Cottage.

Raul Jiménez opened the scoring for Fulham but they failed to capitalise on their lead. Vitalii Mykolenko levelled in first half stoppage time. Michael Keane’s header put Everton in front and a mistake from Bernd Leno allowed Beto to score two minutes later on a day where Brighton and Brentford, who are battling with Fulham for Conference League places, both took three points. Victory for David Moyes’ men was their first since beating Nottingham Forest 1-0 on 12 April.

Two weeks after his crucial goal in Fulham’s fightback at Southampton, Emile Smith Rowe looked full of confidence as he set up the home side’s opener after 17 minutes. He went on a slaloming run down the left and chipped a cross into the penalty area where striker Jiménez rose highest to power a header into the bottom-left corner.

It was all Fulham in the first half but manager Marco Silva, who was serving a touchline ban, would have wanted his men to learn from previous mistakes by converting more chances in order to avoid late heartbreak. Former Everton forward Alex Iwobi was at the heart of Fulham’s best chances. His most notable chance in the 39th minute saw him attempt a curling effort from the edge of the area which did not have enough bend and Jordan Pickford was happy to see it go past a post.

After allowing Jiménez to beat him in the air for the opener, Mykolenko made up for his earlier mishap to level in first half time added on. A corner saw the ball roll out to the left-back on the edge of the box, with his first-time shot deflecting off Andreas Pereira and past Leno into the net.

Everton posed a set-piece threat due to their size and made Fulham rue their missed chances as they took the lead with a second goal from a corner in the 70th minute. Substitute Dwight McNeil’s cross was met by defender Keane at the back post and he nodded in what could well be his final Everton goal with his contract expiring in the summer.

The goal stood after a lengthy VAR review for a potential offside and it was not long before the visitors grabbed a third to stun Craven Cottage. Beto was played through and Fulham keeper Leno made a mistake as he allowed the striker’s side-foot shot to squirm under him and into the net.

Fulham were denied a late penalty for handball by VAR in second half stoppage time as Everton held on for three points.