Fulham are at a fork in the road. Which way do they go? They have plenty of talent, but are they capable of pushing on? Can they convince Marco Silva to extend his contract or will one of the most underrated managers in the Premier League decide it is time to look for a new challenge at the end of the season?

Silva’s itchy feet are a badly kept secret. He has been key to Fulham’s rise since promotion in 2022, but there is a sense of a relationship drawing to a close. The manager, who has been linked with a number of vacancies in recent years, has not been shy to call for more investment in his squad. Oscar Bobb, signed from Manchester City for £27m, was an eye-catching arrival during the winter transfer window. The failure to meet PSV Eindhoven’s asking price for the USA striker Ricardo Pepi was a more frustrating development.

“We have to be more brave, be more aggressive,” Silva said after watching his side throw away a 1-0 lead. He was talking about the dip in Fulham’s performance after a fantastic first half, but he could have been discussing the club as a whole. This was an opportunity for Fulham to cement themselves as genuine contenders for European qualification. The tentative nature of their approach after half-time suggests a slide into mid-table is the likelier outcome.

Kiernan Dewsbury-Hall provided the spark for the late turnaround. The midfielder equalised in the 75th minute and made the winner eight minutes later. Bernd Leno, who was at fault for both goals, was pinned to his line by Jake O’Brien and powerless to do anything more than paw Dewsbury-Hall’s corner into his own net.

Fulham, who were level with Everton at kick-off, had pretty much punched themselves in the face. They were outstanding for 45 minutes but failed to build on going ahead through an unfortunate own goal from Vitalii Mykolenko.

“We should have four more goals,” Silva said. “The game should be over at half-time. The number of chances we created, we have to blame ourselves. Second half, we stopped doing the right things. We expected a reaction from Everton.”

It felt inevitable after a slew of misses from Fulham. They led when Jordan Pickford pushed a shot from Raúl Jiménez on to Mykolenko and the ball went in off the left-back.

Fulham were in their element. Samuel Chukwueze, who linked brilliantly with Alex Iwobi, tested Pickford at the near post and rattled a shot against the bar. Jiménez and Harry Wilson shot wide from good positions. Emile Smith Rowe was also unfortunate not to score when he bent an effort against the woodwork.

Everton’s Vitalii Mykolenko inadvertently diverts the ball into his own net to give Fulham the lead. Photograph: Paul Childs/Action Images/Reuters

Everton, unbeaten in five away games, were overwhelmed but industrious. With one goal in it, they responded with the defiance that typifies every David Moyes side. They stepped up in the second half and imposed themselves. James Garner, Dewsbury-Hall and Idrissa Gueye took control in midfield and Iliman Ndiaye’s dribbles caused problems.

The challenge for the visitors was creating more in open play. James Tarkowski and O’Brien threatened from corners, but Jorge Cuenca and Joachim Andersen kept Thierno Barry quiet before the striker made way for Beto.

With time running out, Everton drew level. Mykolenko broke free down the left and picked out Dewsbury-Hall, whose shot squirmed past Leno.

Fulham, who had been reduced to playing on the break, were unable to lift themselves. Tyrique George, the Chelsea loanee, made an impact after coming on for his Everton debut. The winger won a corner. Everton, dangerous from set pieces all afternoon, completed their comeback when Leno flapped at Dewsbury-Hall’s inswinging cross.

Moyes smiled when he heard about Dewsbury-Hall asking for the goal to be given to him. Everton’s manager had watched events unfold from the back of the new Riverside Stand. It even has a pool on the roof. “I had a wee swim when I was up there,” Moyes deadpanned. Silva was in a less humorous mood.