After a pacy opening to the match, Chelsea had the first half chance of the afternoon when Frank Lampard sent a long pass over to Eden Hazard, but the Belgian failed to control the ball and the chance went begging.
The home fans did not have long to wait for the first goal, however. After build-up play from Roberto Soldado and Eriksen, Sigurdsson skipped past a challenge from Terry before beating Petr Cech in the Chelsea goal.
Spurs continued to create the better chances, although on this occasion Kyle Naughton's right-foot shot was comfortably saved by Cech.
Paulinho came close to adding to the lead, but after seeing his effort beat Cech, it came back off the post.
Chelsea could have equalised just after the restart, but Oscar shot wide after Torres had made his way to the byline and crossed the ball.
Torres, who had been influential in the second period, was then sent off after he was adjudged to have fouled Vertonghen.
Soon after a chance fell to Jermain Defoe, but he scuffed his curling effort and Cech collected easily.
Spurs were inches away from grabbing the win but Sigurdsson's shot flew past Cech's post.