Spurs controlled the game from the first whistle and almost had the lead after 12 minutes after Roberto Soldado hit the post with a cheeky back heel from close range, the chance came about after Johns Ruddy had parried an Christian Eriksen effort to the Spurs man.
The home side continued to press and were rewarded on 28 minutes when Sigurdsson got his first for the afternoon, Soldado and Eriksen again showed great link up play and the ball was put through to Sigurdsson, who duly obliged with a shot into the bottom left hand corner.
Norwich were dominated for large parts of the game and had no complaints when Spurs doubled their lead four minutes into the second half.
Paulinho drove a low cross in from the right and Sigurdsson was left to tap in from close range, however questions will be asked about the goalkeeping of Ruddy for that goal as the ball seemed to go between his hands as he went to the ground.
By the full time whistle Norwich would have had no complaints as Tottenham were certainly better on the day and Spurs will have been buoyed by the performance of debutant Eriksen, especially his link up play with Saldado.
Pedro stepped off the bench to send Chelsea into the FA Cup semi-finals after they beat Leicester 2-1 at the King Power Stadium on Sunday evening.
RB Leipzig came from behind at the Red Bull Arena to end a run of four winless games and defeat Bundesliga leaders Bayern Munich 2-1 on Sunday.