Seamus Coleman grabbed a 75th-minute winner at Goodison Park after the outstanding Rafael van der Vaart had cancelled out Louis Saha's superb early opener.
Both sides had numerous opportunities to win an absorbing contest but it was Everton, rediscovering the spark that has been missing for much of the season, who held on for a victory greeted with much jubilation.
The only consolation for Spurs was that they retained fourth place in the table thanks to yet another defeat for ailing champions Chelsea.
Fans' favourite Robbie Keane was thrown on 10 minutes from time on the day it was confirmed talks had begun over a possible £7million to Birmingham.
But the Republic of Ireland striker could not make a final telling contribution and his Spurs career could now be over.
Spurs were caught cold after just three minutes as Saha finally ended his 11-month league goal drought with a fine strike from 25 yards.
William Gallas backed off his fellow Frenchman outside the area and the striker took full advantage to unleash a ferocious low shot which beat Heurelho Gomes from distance.
The visitors were stung into action and went close as Peter Crouch headed on for Van der Vaart and the Dutchman attempted a left-foot lob from 30 yards which curled narrowly wide.
Everton felt they should have had a penalty after an apparent push by Alan Hutton on Steven Pienaar, but referee Lee Probert saw nothing untoward.
Hutton then compounded Everton's frustration by swinging in the cross from the right which led to Spurs' equaliser after 11 minutes.
Crouch pounced on a Heitinga slip to head the high ball back across goal and Van der Vaart was the first to react, meeting it with a powerful header Tim Howard could not keep out.
Jermaine Beckford had an opportunity for Everton when he turned Gallas inside the box after a neat pass from Saha, but shot well over.
Another shooting chance opened up for Coleman after a slick Everton move but Jermaine Jenas slid in to make a vital block.
Spurs responded as Luka Modric got a sight of goal but Sylvain Distin got in the way.
Crouch thought he had put Spurs ahead on the stroke of half-time when he sidefooted home from a Gareth Bale pass, but the flag was raised for offside.
Van der Vaart then fired narrowly over from a free-kick as Spurs ended the first half in the ascendancy.
Everton boss David Moyes appeared to speak to Probert as the official left the pitch at half-time, possibly about his side's failed penalty appeal, before heading down the tunnel.
But his players remained fully fired up and had the chance to start the second half much as they did the first as Saha released Coleman down the right.
The Irishman raced into the box but ignored Beckford in the middle and shot straight at Gomes.
Spurs suffered a blow as Bale, who had been brought down by Neville while on the charge moments earlier, appeared to limp off after being fouled again just before the hour.
Van der Vaart almost caught Everton out again when he beat Distin on the edge of the box but Howard palmed away his dipping shot.
Everton went straight back onto the attack and Saha met a Coleman cross with a powerful first-time volley but Hutton scrambled back to deflect the goalbound effort wide.
Saha was gifted another chance when a Gallas interception rolled into his path, but Gomes was equal to his shot.
Howard was then called into action twice in quick succession at the other end, first producing a brilliant point-blank save to deny Van der Vaart from six yards after a weaving run by Modric.
Crouch then found space to shoot from distance but Howard tipped the ball over.
Everton threw themselves forward again as Beckford sent Saha clear, and this time it proved decisive.
Saha cut inside and although Gomes parried his long-range piledriver, Coleman followed up to put home the rebound with a diving header.
Ayegbeni Yakubu should have added a third late on when clean through, but dwelt too long on the ball.