Roman Pavlyuchenko scored his sixth goal in four games when he netted the opener in Sunday's Premier League encounter at White Hart Lane, then Luka Modric doubled the lead with a fine second against David Moyes' men.
Harry Redknapp's side, however, had to survive a second-half comeback from the visitors, who scored through Ayegbeni Yakubu and then saw substitute Landon Donovan miss an open goal.
However, defeat dents the visitors' own top-four aspirations, following recent wins over Chelsea and Manchester United.
Spurs are still in the hunt to join the elite but after illness caused them to shut the indoor facilities at their training ground this week, there were memories of four years ago when their hopes were hit by a norovirus on the final day of the season.
On that day, Spurs players could barely make it onto the pitch at West Ham - but against Everton they looked anything but sluggish and did their damage in the first half.
Key performers for Redknapp were Gareth Bale, marauding down the left from full-back, Wilson Palacios crashing into tackles in central midfield and Modric pulling the strings cutting in behind the forwards.
In Pavlyuchenko, Redknapp has a striker who wanted to leave during the January transfer window but now looks like one of the in-form strikers in the country.
He added to his tally in the 11th minute with the opener, set up by strike-partner Jermain Defoe. Defoe chased Tom Huddlestone's long ball down and Sylvain Distin failed to get close enough, allowing the England striker to turn and set his sights on goal.
Whether it was a cross or a shot, Defoe's effort went between John Heitinga and Tim Howard perfectly, allowing Pavlyuchenko to tap in.
The visitors were almost handed an equaliser five minutes later when Leighton Baines' corner was dropped by Heurelho Gomes - Yakubu latched onto the ball but Michael Dawson blocked bravely on the line.
It was a rare opportunity in the first half for Moyes' men, who did not have Louis Saha in the matchday squad and saw Yakubu and Victor Anichebe struggle to impose themselves on Spurs' defence.
Spurs continued to attack after the opener, with Howard kept busy with further efforts from Pavlyuchenko and Niko Kranjcar before Modric struck.
Modric's goal, just before the half-hour mark, was a fine finish to cap off a slick move involving all three of Redknapp's Croatia players.
It started with Modric interchanging passes with Vedran Corluka. Kranjcar then fed Modric just inside the penalty area and he curled an effort went in off the underside of the crossbar.
Jack Rodwell came close with a header for Everton just before the break, while Bale had an effort deflected wide at the other end to bring an end to an entertaining first half.
Moyes changed things at half-time, bringing on Phil Jagielka for Leon Osman, then he saw Heitinga test Gomes with a powerful drive just after the restart.
Huddlestone went close with a volley but he caught Heitinga with his follow-through and was carried off on a stretcher after appearing to hurt his shin.
With Younes Kaboul brought on, Everton pulled a goal back shortly afterwards. Mikel Arteta's corner went to the far post, Rodwell headed back across goal, with Anichebe holding off Gomes and allowing Yakubu to tap in.
Everton could have been level a minute later when Rodwell caught Phil Neville's cross with a first-time volley - but Gomes was down sharply to save.
Sensing the game being there for the taking, Moyes took off Anichebe and brought on Donovan.
Everton had an opportunity to level in the latter stages when Palacios gave the ball away and Steven Pienaar raced on - but Gomes was equal to the finish.
Donovan also embarrassingly missed his open goal, when he got on the end of Rodwell's cross.
Palacios stuck the ball in the net at the death - but it was after the final whistle.