The former Reading attacker's late well-taken goal secured his side a draw against David Moyes' side in a thoroughly entertaining 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 reigning Premier League Player of the Month Jan Vertonghen, before Phil Jagielka drew the visitors level after a quarter of an hour.
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 American goalkeeper Tim Howard after evading the attention of Sylvain Distain.
Everton reacted well to going behind though, and in the 15th minute the Toffees made their pressure pay when Jagielka equalized from a corner. The center back rose highest at the back post to head Leighton Baines' lofted cross past the despairing dive of Hugo Lloris.
After Mousa Dembele and Vertonghen had impressed in the first half, it was Everton's own Belgium international, Mirallas, that lit up the game soon 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. He left a cluster of Spurs defenders trailing as he twisted and turned his way into the box on the right, before firing a crisp low shot into the bottom left corner and past Lloris.
Minutes later Spurs thought they had equalized 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 leveling 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 third, two points ahead of Arsenal, but they have played a game more than their North London rivals. Everton remains in sixth place, six points behind Tottenham after missing a chance to close the gap on the race for a Champions League berth.