The midfielder wasted little time in showing the shooting prowess he demonstrated in the second half of last season on loan at Swansea with a fine strike 10 minutes into the second half - and just 10 minutes into his Spurs career.
Andros Townsend darted down the left and cut the ball back for Sigurdsson who, in an instant, controlled and drilled low across home goalkeeper Steve Arnold.
Yago Falque secured the victory two minutes from time, latching onto Adam Smith's pass and driving into the box before finding the far corner.
The message afterwards from Andre Villas-Boas was very much 'objectives achieved' and there were plenty of positives on the night.
As well as Sigurdsson's fine strike, Jan Vertonghen looked assured on his debut in the second half and there were successful returns from injury for Michael Dawson and Tom Huddlestone, the latter out of action since last August due to ankle problems.
Townsend was a constant threat in the second half and there was another debutant - young development squad striker Souleymane Coulibaly, who certainly didn't seem overawed by such an occasion.
We were always in control in terms of possession but chances were few and far between in the first half.
Indeed, the only save came in the 25th minute as ex-Spur Chris Day went full length to his right to touch wide Harry Kane's shot after good work from Steven Pienaar. Kane led the line in a 4-2-3-1 formation.
There were seven changes at the interval including those debuts for Vertonghen, Sigurdsson and Coulibaly with Kyle Walker, Jermaine Jenas, Aaron Lennon and Kane staying on for another 15 minutes in the second half.
By then, we were 1-0 up with Sigurdsson striking home impressively after Townsend showed his raw pace to get to the left byline.
Tom Carroll had earlier forced the save of the match from Arnold and he was involved in the next chance, releasing Townsend again down the left to tee-up Kane, only for the striker to fire over.
Townsend also set-up Coulibaly, who was narrowly wide from a tight angle before being sent clear on goal by Sigurdsson in the 71st minute, this time Arnold did well to block with his legs one-on-one.
As the clock ticked into the 88th minute, Adam Smith sent fellow substitute Falque away down the right and the youngster showed composure to switch onto his left foot and find the bottom corner from just inside the box.
Stevenage - 1st half (4-4-1-1) - Day; Gray, Ashton, Roberts, Charles; Morais, Dunne, Grant, Freeman; Ajose; Haber.
2nd half - (4-4-1-1) - Arnold; Shelley, N'Gala, Furlonge, Hills; Marum, Tansey, Ball, Carr; Shroot; Thalassitis.
Spurs - 1st half (4-2-3-1) - Cudicini; Walker, Dawson, Kaboul, Naughton; Jenas, Livermore; Lennon, Bentley, Pienaar; Kane.
2nd half - (4-2-3-1) - Friedel; Walker (Smith, 62), Gallas, Vertonghen, Bassong; Jenas (Huddlestone, 62), Carroll; Lennon (Falque, 62), Sigurdsson, Townsend; Kane (Coulibaly, 62).
Goals: Spurs - Sigurdsson (55), Falque (88).
Referee: Mr D Deadman.