Spurs reinforced their midfield in the close-season by signing the likes of Paulinho and Etienne Capoue, leaving existing players like Sigurdsson with a point to prove.
And the Iceland international did his prospects of earning a regular first-team spot no harm with a fine performance at White Hart Lane, which he capped with a goal either side of half-time.
"Sigurdsson is a big fighter in this squad, always hoping for his opportunity to arrive," Villas-Boas said.
"When it does arrive, he puts on performances like this. It was the same for him last season, in February and March. We saw his best level today."
Sigurdsson was teed up by debutant Christian Eriksen for his first goal and Villas Boas was also impressed with the Denmark international, who was withdrawn late in the game to a standing ovation from the home crowd.
"Eriksen already has so much experience from Ajax," added the Portuguese. "He really linked the game well for us in the final third today. It's easy for him to find his passes when his quality is so good."
The former Ajax player was also pleased with his own performance and believes Tottenham can go on to challenge for honours.
"It felt really good. I'm really happy to be here," he said
"Hopefully [Tottenham will mount a title challenge] this season, or maybe after. But this is an exciting season.
"They [the fans] can expect great things, they're allowed. We'll try to do our best."