With this result Tottenham Hotspur moved from championship outsiders to serious pretenders. History and the odds say that Harry Redknapp's band may well fall away, and the manager's mantra remains that they have a chance and nothing else. But by winning this game in hand without Scott Parker, Ledley King or Sandro, Spurs sent a message to Manchester United and the league leaders Manchester City, who they are now only three points behind.
A pleased Redknapp kept to his party line but he did say: "I think the pressure's on Man City. You look at the money they've been able to spend – they're going to be expected to be there, certainly them or Man United. We're just hanging in there, keeping the players bright, keeping players enjoying it, making sure we don't leave it all on the training ground.
"We're playing with smiles on our faces. At the moment we can enjoy it. When you're struggling at the bottom that's pressure."
Tottenham will have the chance to close that gap on the blue billionaires when Roberto Mancini's side welcome them on Sunday week, a contest that will offer the best barometer yet of their title credentials.
For Redknapp, though, it is all about the next encounter. He said: "I [will not] look any further than Wolves on Saturday. I know we're level with Manchester United and three points behind Manchester City but all I will think about driving home is Wolves. We've got a really hard game on Saturday and we've just got to keep taking each one as it comes.
"I've been saying all along it's not impossible to win the title but it's very, very hard. But we're in there, we've got a chance. I wouldn't put that pressure on the players. They believe we've got a chance – we've got good players, good spirit. William Gallas came in [the other day] and said: 'We've got a chance here.' It's not beyond the realms of possibility. We've got some real quality, haven't we?"
Clear on Wednesday night was the calibre of the goal that sealed this triumph: a 30-yard piledriver from Benoît Assou-Ekotto after 63 minutes that arrowed from left to right to kill the visitors' resistance, and further reiterate the quality that Redknapp has assembled.
David Moyes's project each year is to produce an Everton team of overachievers. This season's is a work in progress as the Toffees arrived in north London in the midst of patchy run that had yielded only two wins from their previous five league outings to stand in 11th.
They did, though, come close to the fillip of a perfect start when Younès Kaboul's mistake in front of Brad Friedel allowed Louis Saha to send a shot skimming over the turf, but it was wide.
The error was soon mirrored at the opposite end. Tim Cahill lost possession too near to Tim Howard and for a moment an opportunity glimmered for Luka Modric, but the chance was not realised.
This breathless start presaged a fast, slick and quick-witted offering from Spurs that became the story of the first half as their brand of sweetly-muscular movement and passing left Everton as spectators hoping to somehow force themselves into the contest.
Emmanuel Adebayor's best chance arrived after Kyle Walker had taken a tumble near halfway. When the match restarted a Rafael van der Vaart pass sent Gareth Bale charging down the right. He made the correct decision to slide the ball to Adebayor, but the striker's flip over Howard was clumsy.
Van der Vaart nearly proved more lethal from 25 yards. Walker served a pass into Modric and when he relayed the ball to Bale the Welshman allowed it to pass and there was the Dutchman to let fly with a left-foot curler that landed on the roof of the net.
Ten minutes from the break Spurs finally had the advantage they deserved. Assou-Ekotto put up a high diagonal – Leighton Baines should have thumped it clear but his air shot allowed Aaron Lennon, who had been quiet thus far, to cut inside the left-back and when the shot rolled off his boot it passed under Sylvain Distin to wrong-foot Howard.
Any attempt to stem the white tide by Moyes at half time did not work. Within minutes of the restart Bale had acres to sprint into, and when he smashed an effort at Howard the American parried well despite a deflection. Lennon then ghosted into the far post to head Assou-Ekotto's delivery wide of Everton's woodwork as the sense hardened that only by throwing the match away could Spurs fail to end the evening in profit.
Before kick-off Redknapp had said: "We have to keep believing and you never know. We can give ourselves a chance to have an amazing second half of the season."