The Icelandic international was on hand to convert two excellent team goals - having only scored three in his previous 35 league matches in our colours - as we dominated throughout and kept another clean sheet, our fifth in six matches in all competitions this season.
And while Sigurdsson will rightly grab the plaudits for his goals, the performance of debut-making Christian Eriksen certainly caught the eye as he impressed with his creativity.
Andre made two changes from the defeat at Arsenal, with Eriksen coming into the side for his Spurs bow following his move from Ajax, along with Sigurdsson, the pair replacing Nacer Chadli and Etienne Capoue.
We started on the front foot right from the opening whistle with Sigurdsson and Andros Townsend both firing in efforts from distance although neither troubled Norwich goalkeeper John Ruddy.
It was one-way traffic for the majority of the half as we dominated possession with Eriksen to the fore, while the attacking intent from full-backs Kyle Walker and Danny Rose ensured the visitors were pegged back in their own half for long periods.
We went so close to opening the scoring on 12 minutes after some magical skill from Eriksen, who glided into the box, beat two men with close control and drilled in a shot which Ruddy saved. The rebound fell to Roberto Soldado whose audacious backheel was cleared off the line by former Spur Sebastien Bassong.
And the Canaries skipper was there to deny us again on 25 minutes, diving in to divert Soldado’s shot over the bar after excellent work from Mousa Dembele to get to the byline and cut back a cross.
Three minutes later we were in front…and it was a fantastic team goal. Dembele sprayed the ball out wide to Rose, he drilled in a cross which Soldado controlled on his chest before touching off to Eriksen. The Dane played a delightfully weighted ball for Sigurdsson to run on to and curl into the far corner with his right foot.
Despite our dominance though, we needed Rose to show all his defensive qualities to keep us ahead on 36 minutes. Nathan Redmond whipped in an inviting cross from the left, Ricky Van Wolfswinkel looked set to poke home but across came Rose to put him under pressure with a sliding tackle and he might even have got the slightest touch to send the ball wide, although a goalkick was awarded by referee Lee Mason.
The second period was just four minutes old when we doubled our advantage, our Icelandic international once again on the scoresheet. It was another good goal too, a patient build-up ending with Eriksen finding Paulinho out wide on the right and he had time to deliver a low cross which Sigurdsson turned in from four yards out.
And it needed a smart save from Ruddy to deny Sigurdsson his hat-trick just after the hour when he palmed away a fierce 20-yard drive from the midfielder.
Having been thankful to Rose in the first half, we were indebted to the full-back again on 69 minutes when he again prevented Van Wolfswinkel. Hugo Lloris punched clear a free-kick, Redmond fired in the rebound which fell to the Norwich striker eight yards out in front of goal, he took a touch and that allowed Rose to slide in and block when he eventually fired off his shot.
Andre shuffled his pack late on, bringing on Lewis Holtby, Sandro and Erik Lamela - the Argentinian making his home debut - in place of Eriksen, Sigurdsson and Dembele respectively.
There was drama five minutes from time when Lloris punched away a long ball but it was adjudged to be outside the area. Robert Snodgrass lined up the free-kick but his effort cannoned off the wall to safety and that was the last of the action.
Spurs: Lloris, Walker, Dawson, Vertonghen, Rose, Dembele (Lamela 83), Paulinho, Eriksen (Holtby 71), Townsend, Sigurdsson (Sandro 79), Soldado. Substitutes (not used): Friedel, Naughton, Kaboul, Defoe.
Norwich: Ruddy, Whittaker, Bassong, Turner, Garrido, Snodgrass, Fer, Johnson (Howson 65), Redmond (Pilkington 74), Elmander (Tettey 74), Van Wolfswinkel. Substitutes (not used): Bunn, Olsson, Martin, Hooper.
Goals: Spurs - Sigurdsson 28, 49.
Yellows: Spurs - Lloris. Norwich - Johnson, Garrido, Elmander.
Referee: Lee Mason.