The Icelandic midifelder scored on his Spurs' debut as Andre Villas Boas' side eased to a 2-0 win over the League One side.
The midfielder, who spent the second half of last season on loan at Swansea City, made an instant impact after coming on as a subsitute in the second, as he drilled home the opening goal of the game from Andros Townsend's corner. 22-year-old Spanish midfielder Iago Falque made it 2-0 just before full time to make sure of the win.
New boss Andre Villas Boas named a strong side ahead of the game with the League One side, with Matt Dawson, David Bentley, Aaron Lennon and Steven Pienaar all involved as they prepare for the new campaign.
However, it was 18-year-old Harry Kane who proved to be at the centre of most of the Tottenham play, the striker twice going close inside the opening 30 minutes. First, he was denied by a stunning stop from Stevenage keeper Chris Day after latching onto a through ball from Pienaar, before the youngster nodded a diving header just wide from a pinpoint cross from Kyle Walker.
Despite dominating much of the first half Spurs were unable to break the deadlock and the two teams headed to the break all square.
Villas Boas made a number of changes during the interval, introducing both Sigurdsson and fellow new boy Jan Vertonghen to the fray.
It didn't take long for the Icelandic international to make an impact, as he fired home fiercely from Townsend's corner 10 minutes into the second half.
Spurs' dominance was absolute despite making a large number of changes, and they were denied a second 18 minutes from time when Souleymane Coulibaly's effort was well saved by Steve Arnold after being put through by Sigurdsson.
The North Londoners did grab a second two minutes from time however, as Falque broke free down the right before firing a left footed strike into the bottom corner to put the gloss on a confident display.