Everton came from behind to beat Fulham 2-1 late on at Craven Cottage as David Moyes' side moved up to eighth place in the Premier League, just two points behind Liverpool.
With the suspended Moyes watching from the stands, alongside watching England manager Thomas Tuchel, the visitors had appeared on course for defeat as they trailed to Vitalii Mykolenko's first-half own goal with just a quarter of an hour left in west London.
However, strikes from Kiernan Dewsbury-Hall, followed by Bernd Leno's horror own goal, saw Everton jump up the table, with Liverpool now very much in sight ahead of the champions' home game with Man City on Super Sunday.
And given Everton rank sixth for points won since Moyes returned to the club last January, do not be shocked if the Toffees are able to overtake their rivals and reach Europe come the end of the season.
It could have been the other way round, though, with Fulham up to seventh had they been more clinical in the first half and built on the 18th-minute lead given to them via Mykolenko's unfortunate own goal.
However, those spurned openings came back to haunt them as Everton - who brought on their January loan signing from Chelsea, Tyrique George - stepped up the pace in the second period, firstly levelling via Dewsbury-Hall's well-taken effort, before claiming all three points after a second bizarre own goal of the game.
There appeared little danger as Dewsbury-Hall's 83rd-minute corner floated Leno's way, but under minimal pressure from Jake O'Brien, the experienced German goalkeeper somehow punched the ball into his own net.
Silvar reacted by throwing on his ÂŁ27 million deadline-day signing from Man City, Oscar Bobb, but with little time to impact the game, the visitors held on and Moyes' dream of European football next season is maybe not so outlandish after all.
Fulham boss Marco Silva:
"He [Jake O'Brien] was interfering [for Everton's winner], but to be honest, I am so disappointed and we should be disappointed with ourselves much more than talk about the referee.
"It is really the moment to look for us. We have to be more brave, to be more aggressive in all the moments we conceded the goals."
Everton boss David Moyes:
"We did well to make sure it was only 1-0 at half-time and we played much better in the second half.
"The idea now is to try and push on, but every win you get in the Premier League, you get quite excited and then you lose a game and can easily be at the wrong end of the league.
"It wasn't fun watching it up there.
"It is a bit sad if you're going to get that for showing emotion if you like. No doubt I broke the rules. No doubt I ran on the pitch, but just check how many people from the Arsenal bench ran on the pitch when they scored the other night."
Analysis by Your Site' Rich Morgan:
Everton manager David Moyes was not sure whether to talk up his side's European prospects or play them down after their late come-from-behind win at Fulham, and instead ended up doing both!
"Hugely important [win] and I think it probably keeps us away from the big R word at the bottom of the league, that's for sure," he initially said after the game without a hint of sarcasm, before revealing his true feelings.
"I don't want to come in here and say we're trying to avoid relegation. I don't want to do that because Everton have had too much bad news and bad publicity, so I'd rather come in here and say we're having a go at Europe.
"You might laugh at me in a few weeks' time and say, 'How stupid was I', but I'd rather be positive."
However, with the Toffees now in a tightly congested pack hot on the tails of sixth-placed Liverpool, Moyes and his players really can dare to dream of a first European appearance for nine seasons and why not, given their impressive form since the Scot returned to manage the club last January.
In fact, Everton rank sixth for points won in that time, so do not be shocked if that is where they finish come May.
