Tottenham arrived at Goodison for this re-arranged Premiership fixture courtesy of bye in the UEFA Cup.
If David Moyes' men wanted to emulate their capital cousins and appear in next year's competition then it was vital they took something from this game.
Spurs, though, arrived in a buoyant mood after thumping Fulham 4-0 in the FA Cup at the weekend.
Everton's talismanic striker Andy Johnson was out injured and Tim Cahill suspended so Victor Anichebe and James Beattie formed the two-pronged attack.
Tottenham brought the game to Everton from the first minute with Young-Pyo Lee and Teemu Tainio creating space in the middle of the park for Aaron Lennon and Dimitar Berbatov to receive some probing balls, but not one shot was actually fired towards Tim Howard's goal in the opening exchanges.
In reply, Everton's Phil Neville floated a stunning cross towards the Spurs goal but no-one was the near the ball to capitalise.
Everton started to find their feet as the game progressed but Spurs still looked the more threatening.
Referee Uriah Rennie booked Anichebe for what was essentially the first tackle of the game. Moments later, Neville followed the youngster into the book for a foul on Berbatov after the Bulgarian had gone down theatrically.
Everton had the first real chance on 20 minutes after a cross by Mikel Arteta found Leon Osman ten yards from Paul Robinson's goal, but the midfielder got the ball hopelessly tangled in his legs and the threat was lost.
On 23 minutes Osman spurned another chance by shooting inches wide and then Beattie narrowly missed the upright as the game briefly came to life.
Spurs and Everton exchanged pot shots without any real purpose until Berbatov put the visitors ahead after Osman squandered possession far too easily.
Lennon sped up the pitch to cross for the Bulgarian who made no mistake from 15 yards.
But Arteta equalised under controversial circumstances with a fantastic free-kick on 42 minutes.
The Spurs players were furious after the linesman had flagged for a foul on Michael Dawson, but Rennie saw a foul against Anichebe and gave the kick to the home side.
Everton upped the pace in the second half and Beattie in particular began enjoying his most penetrative game for a long while with support from Osman and Arteta.
Spurs were not ready to lie down but in truth the game became increasingly scrappy.
Lennon was replaced by Steed Malbranque with ten minutes to go as Martin Jol attempted to kick-start his side, who had been under pressure for most of the second half.
The switch almost paid dividends as Jermaine Jenas received the ball from the substitute to set up Berbatov who fired over much to Everton's relief.
Robbie Keane wasted the chance of the half as Alan Stubbs slipped and the Irishman ran clear but fired over Howard's bar as Joseph Yobo slid in for the block.
Joleon Lescott should have won the game on 85 minutes but inexplicably chose to pass instead of hitting the shot himself.
Spurs sealed an unlikely victory on the stroke of full-time after Jenas latched on to a Malbranque pass and fired past an outstretched Howard.
The goal was probably the only bit of excitement in an otherwise lacklustre clash.