The Spaniard stroked home a penalty winner against Crystal Palace at Selhurst Park and repeated the feat at White Hart Lane to maintain his new club's perfect start to the seasonRoberto Soldado struck again from the spot as Tottenham Hotspur made it two wins out of two in the Premier League with a 1-0 defeat of Swansea.
The Spain international, who also scored twice in midweek against Dinamo Tbilisi, converted from 12 yards out early in the second half to wrap up the points, after Jonjo Shelvey had felled Andros Townsend in the area.
It was a first Premier League start for Tottenham for Townsend, while Etienne Capoue - signed from Toulouse earlier in the month - made his home debut, after being preferred in midfield to Gylfi Sigurdsson.
Michael Laudrup opted to leave Wilfried Bony - scorer in the 4-1 defeat to Manchester United last week - on the bench, with Michu named as the visitors' lone striker.
Both sides were reduced to efforts from outside the box in the early stages, Paulinho and Capoue testing the reflexes of Michel Vorm, while former Tottenham winger Wayne Routledge forced a good save from Hugo Lloris.
It took 20 minutes for the hosts to fashion the game's first real chance and they almost took the lead in fortuitous circumstances.
Swansea captain Ashley Williams headed against his own near post from Kyle Walker's right-wing cross and Paulinho reacted quickest to the rebound, but his driven shot was brilliantly kept out by Netherlands international Vorm.
The visitors were undeterred by that scare and continued to press forward, Shelvey keeping Lloris on his toes with a low effort that the Frenchman tipped wide.
Laudrup's men appeared to struggle in defence, however, and they were grateful to Vorm once more as he pulled off another acrobatic save to deny Moussa Dembele after more good work down the right by Walker.
Walker forced another save from Vorm before Paulinho fired over from close range, but the real talking point came in the final minute of the first half, with referee Neil Swarbrick awarding a free kick after Shelvey had clearly fouled Townsend inside the box.
Villas-Boas' side may have felt aggrieved by that decision, but they did not allow it to affect their attacking mentality, Townsend curling inches over from distance shortly after the interval.
Tottenham were finally rewarded 12 minutes into the second half, Shelvey again adjudged to have clipped Townsend inside the area, but this time Swarbrick did point to the spot.
Soldado made no mistake, replicating his winner at Crystal Palace last Sunday by scoring from 12 yards with a calm finish into the bottom corner.
Swansea still posed a danger in spite of that setback, and came close to levelling when Pablo Hernandez curled wide from the edge of the box.
Chico Flores stung the palms of Lloris with a vicious volley but, although Laudrup threw Bony into the action in search of a leveller - Tottenham held on with little difficulty, with Paulinho denied by Vorm at the death.