The former Reading attacker's well-taken goal late on secured his side a draw against David Moyes' Toffees in a thoroughly entertaining Premier League contest in north London
The visitors looked to have fought back brilliantly to secure a surprise win after going a goal down early on, before Tottenham's Icelandic midfielder struck in the dying stages.
A fabulous individual goal in the second half from Kevin Mirallas had made it 2-1 to the Toffees after a frantic opening to the match. Emmanuel Adebayor had put Tottenham ahead in the first minute following brilliant play by Jan Vertonghen, before Phil Jagielka drew the visitors level after a quarter of an hour.
Previews for this match were dominated by the injury suffered by Gareth Bale against Basel on Thursday, and his absence certainly affected Tottenham as their Champions League qualification aspirations were knocked slighty off course by an in-form Everton side.
The Welshman has been pivotal for the Lilywhites this season - the last time Spurs won a match that he has not scored in was all the way back on New Year's Day when they beat Reading 3-1.
The hosts were also without Aaron Lennon and Jermain Defoe, while David Moyes was forced into making changes as Marouane Fellaini and Steven Pienaar served suspensions.
Latecomers to the ground will have cursed their poor time management as the home side took just 33 seconds to take the lead. Villas-Boas' men made a blistering start to the game to go 1-0 up through Adebayor, as the Togo international diverted Vertonghen's enticing cross past Tim Howard after evading the attention of Sylvain Distin.
Everton reacted well to going behind though, and in the 15th minute they made their pressure pay when Jagielka equalised from a corner. The former Sheffield United centre-back rose highest at the back post to head Leighton Baines' lofted cross past the despairing dive of Hugo Lloris.
The home team wanted a penalty shortly before the break when Clint Dempsey's cross from the right was blocked in unorthodox fashion by the chest of Darron Gibson, but had their appeals promptly dismissed by Andre Marriner to a chorus of boos from the Spurs faithful.
After Mousa Dembele and Vertonghen had impressed in the first half, it was Everton's own Belgium international, Mirallas, that lit up the game after the interval.
Fresh from his wonderful solo effort against Stoke City last weekend, Mirallas repeated the trick with a magnificent goal in the 53rd minute to put Everton ahead. The 25-year-old left a cluster of Spurs defenders trailing in his wake, twisting and turning his way into the box on the right before firing a crisp low shot into the bottom left corner.
Minutes later Spurs thought they had equalised through Dembele, only for his deflected effort from distance to be tipped on to the crossbar brilliantly by Howard.
Villas-Boas' side continued to threaten and both Kyle Walker and Dempsey came close to levelling midway through the half, before Sigurdsson smashed a shot past Howard to make it 2-2 after an effort from Adebayor had crashed back off the post and into his path.
Spurs remain in fourth, two points ahead of Arsenal, but they have played a game more than their north London rivals.