Suspended for Wednesday night's Champions League defeat at Inter Milan, Van der Vaart scored his fifth goal in as many games to send Spurs third in the Premier League.
The Holland midfielder's effort cancelled out Leighton Baines' brilliant free-kick - his first goal for almost 14 months - while Peter Crouch wasted more than one chance to seal what would have been Tottenham's fourth comeback win in five league matches.
Today's game kicked off barely 48 hours after Spurs got back from Milan and, once again, the words 'European hangover' lingered in the air in north London.
But with third place - and even second - up for grabs for 24 hours at least, there was no shortage of motivation for Redknapp's men.
It looked as if they were really going to have to work for it, though, as Everton, without Mikel Arteta, chased and harried all over the pitch.
Spurs midfielder Wilson Palacios, starting his first league game for six weeks, was rightly booked for a foul on Ayegbeni Yakubu as the visitors looked to hit their opponents on the break.
But Tim Cahill's tame long-ranger and Luka Modric's low strike from the edge of the box - well saved by Tim Howard - were the only efforts on goal until Baines struck in the 17th minute.
The fit-again Younes Kaboul fouled Yakubu on the edge of the box and Baines stepped up to curl a delightful free-kick into the top corner.
But Tottenham were level inside three minutes after Howard flapped at Alan Hutton's cross and Crouch nodded the ball back across goal for who else but Van der Vaart to blast over the line.
Modric, captain for the day in the absence of Ledley King and Tom Huddlestone, fired wide from 20 yards and Crouch saw a penalty appeal turned down after getting sandwiched between Phil Jagielka and Phil Neville.
Baines curled over another free-kick from a near-identical position from where he had scored and Crouch sent a weak header straight at Howard from Hutton's cross in first-half stoppage-time.
Spurs withdrew Palacios for Sandro during the interval, with Crouch's scuffed shot the first effort of the second half.
Substitute Sandro almost laid on a 52nd-minute goal for man-of-the-moment Gareth Bale, whose flicked header was cleared behind by Jagielka despite being just off target.
That was moments after Seamus Coleman became the first Everton player booked for bringing down Aaron Lennon as Tottenham broke.
Crouch almost deflected a John Heitinga free-kick into his own net before the visitors were forced to bring off a hobbling Yakubu for Louis Saha just past the hour mark.
The fit-again Steven Pienaar sliced high a wide from 25 yards but it was not happening for either side and Spurs decided to introduce Roman Pavlyuchenko for Lennon in the 69th minute.
Bale switched to the right and he and Sandro immediately set up Crouch for a weak effort at Howard, with Cahill just off target with a snapshot at the other end.
Van der Vaart was booked after furiously protesting the award of a goal-kick when he looked to have won a corner.
Pavlyuchenko saw his finish blocked behind by Sylvain Distin following a Spurs break and Sandro was yellow carded for felling Saha as he tried to do the same.
Tony Hibbert replaced Heitinga for the final 12 minutes, shortly before Coleman was withdrawn for Jermaine Beckford.
With two minutes remaining, Van der Vaart looked to have a chance to snatch all three points but his shot on the turn was blocked by Distin and Hibbert.