The full-back raised the roof at White Hart Lane with an absolute scorcher in the 63rd minute.
Picking the ball up 35 yards out, there was nothing on for Assou-Ekotto, so he decided to have a go himself - and the ball flew past Tim Howard into the top corner.
The goal put us out of reach of an Everton team packed full of attacking talent but one that rarely threatened Brad Friedel on the night.
We were already well on top when Aaron Lennon made the key breakthrough in the 35th minute and there was no coming back from Assou-Ekotto's wonder goal.
The win made it 14 wins, three draws and just one defeat in our last 18 matches in the Premier League and took us level with Manchester United on 45 points.
Harry Redknapp made eight changes from Saturday's FA Cup win against Cheltenham and three from the previous Premier League outing against West Brom on January 3.
Michael Dawson and Lennon returned to Premier League action and Jake Livermore started alongside Luka Modric in central midfield.
There was a chance for Everton inside the first minute as Landon Donovan's cross was cleared to Louis Saha, who dragged his shot across goal from 16 yards.
That was as close as the visitors came as we dominated the first half.
Emmanuel Adebayor, Rafa van der Vaart and Modric all shot wide then a lightning break, van der Vaart released Bale, he found Adebayor who skipped around Tim Howard but ran out of room.
Adebayor then poked just wide from Assou-Ekotto's cross and van der Vaart dipped a first-time curler from 20 yards onto the roof of the net.
Lennon was soon on hand to open the scoring. Assou-Ekotto switched play from left to right with a sweeping 50-yard crossfield pass that Lennon took inside Leighton Baines, dribbled across Sylvain Distin and then hit low past Howard from 16 yards.
We started the second half brightly and Howard did well to turn away Bale's deflected shot after a typical 50-yard burst from the Welshman.
Lennon couldn't direct a fine cross from Assou-Ekotto on target after 54 minutes and a minute later, Saha angled wide from Baines' near-post cross.
You always sensed a second goal would be enough for us and it arrived in style courtesy of Assou-Ekotto's left foot in the 63rd minute.
Bale fizzed a shot just over as we clicked into gear.
Kyle Walker burst down the right before finding van der Vaart, he slipped through to Adebayor but Baines threw himself in to block.
Lennon and Adebayor then combined, Adebayor saw another shot blocked and van der Vaart's follow up was deflected over. It was one-way traffic at this point.
Steven Pienaar replaced Lennon on 78 minutes and looked lively against his old club, almost setting up Adebayor.
Dawson and Younes Kaboul remained in control at the back while Livermore, who really shone on the night, continued to break up play centrally.
Everton wasted their final chance of a consolation when Saha blazed over from close range in added time.
It was that sort of night for the visitors but we keep marching on.
Spurs (4-4-1-1): Friedel; Walker, Dawson, Kaboul, Assou-Ekotto; Lennon (Pienaar, 78), Livermore, Modric, Bale; Van der Vaart; Adebayor (Pavlyuchenko, 86). Subs: Cudicini, Bassong, Rose, Kranjcar, Defoe.
Everton (4-4-1-1): Howard; Neville, Distin (Duffy, 59), Heitinga, Baines; Donovan, Cahill, Fellaini, Bilyaletdinov (Gueye, 82); Anichebe (Drenthe, 68); Saha. Subs: Mucha, Stracqualursi, McFadden, Vellios.
Goals: Spurs - Lennon (35), Assou-Ekotto (63).
Referee: Mr M Atki