Spurs were frustrated for large periods of the match at White Hart Lane before Belgian defender Jan Vertonghen clinched the points in the 75th minute.
Swansea began the match on the front foot, although Hugo Lloris was untroubled in Spurs’ goal and it was the home side who threatened first through in-form Jermain Defoe.
The England international latched onto Emmanuel Adebayor’s through-ball only for Gerhard Tremmel to make the save from his right-footed shot while Michu made the block to deny the striker after he had initially conceded possession.
Adebayor’s close-range effort was then blocked by Chico from Kyle Walker’s cross, Defoe’s turn and shot drifted wide of Tremmel’s goal while Walker’s long-range special was straight at the Swansea keeper.
The Swans did offer a threat of their own when Jonathan de Guzman lashed a shot just over Lloris’ goal while Michu was close to catching out the French keeper from distance after Mousa Dembele lost possession.
Swansea came within a whisker of getting their noses in front minutes into the second half, but Nathan Dyer could not hit the target after Wayne Routledge did well to better Gallas and play in a teasing cross.
Adebayor then saw a long-range effort parried for a corner by Tremmel while Defoe’s left-footed strike in the 66th minute was always curling away from the far post.
Tottenham suffered an injury blow when Adebayor hobbled from the field of play, although it was unclear whether the former Manchester City and Arsenal man had suffered an ankle knock or hamstring strain.
The breakthrough finally came in the 75th minute when the unmarked Vertonghen guided home Walker’s free-kick past Tremmel into the far corner of the net.