The north London side secured a deserved win over the Welsh side, with the summer signing netting the only goal after Jonjo Shelvey felled Andros Townsend inside the area
The Spain international, who also scored twice in midweek against Dinamo Tbilisi, converted from the spot early in the second half to wrap up the points after Jonjo Shelvey had brought down Andros Townsend in the area.
Townsend was handed his first Premier League start for Tottenham by manager Andre Villas-Boas, while Etienne Capoue - signed from Toulouse earlier in the month - made his home debut as he was 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 defense, 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 it did not allow it to affect its attacking mentality, Townsend curling inches over from distance shortly after the interval.
Tottenham was finally rewarded 12 minutes into the second half, Shelvey again adjudged to have clipped Townsend inside the area, however 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 leveling 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 leveler - Tottenham held on with little difficulty, with Paulinho denied by Vorm at the death.