The Belgian struck a sweet half-volley 15 minutes from time to decide a drab game and lift Spurs back into the Champions League places.
The Belgian center back celebrated his strike by pretending to rip open his shirt Superman-style after saving a Spurs team that had until that moment lacked attacking verve in an unremarkable game at White Hart Lane.
Yet Tottenham got the job done against in-form Swansea, Vertonghen sweeping in a half-volley with his weaker right foot from Kyle Walker's free kick as Spurs climbed into fourth place ahead of the busy Christmas period.
Spurs manager Andre Villas-Boas will be equally relieved that his players were able to keep a clean sheet and avoid their habit of conceding in the last 10 minutes of matches against a Swansea side that offered little in the final third.
Tottenham made one change to the starting XI that lost the club's previous outing at Everton, bringing in Kyle Naughton for Steven Caulker as Gareth Bale failed to recover in time from a hamstring injury, while Swansea made two changes to the team that was beaten by Norwich as Leon Britton returned to the heart of Michael Laudrup’s midfield.
The pre-match talk was of an open game between two attacking teams, but neither side played with any purpose during a drab opening period in which the home side created the better chances but barely tested Swansea goalkeeper Gerhard Tremmel.
In the 12th minute, Michu brilliantly blocked Jermain Defoe’s goal-bound effort before Swansea defender Chico Flores denied Emmanuel Adebayor in similar fashion.
At the other end, Michu went closest for the visitors with a stunning effort from just inside the Spurs half that had Hugo Lloris scrambling before the ball drifted just over the crossbar.
Swansea came out for the second half with more purpose and should have broken the deadlock two minutes after the re-start. Wayne Routledge skipped into the Tottenham penalty area and crossed for Nathan Dyer, who should have scored from five yards but took his eye off the ball and headed wide.
Adebayor forced Tremmel into action and Walker shot off target before Spurs opened the scoring in the 75th minute just when the game appeared to be meandering towards a goalless draw.
For all the pretty passing on display, it was a rudimentary set piece that did the job. Walker whipped in a free kick that glanced off a Swansea player’s head before landing at Vertonghen, who swept home with his weaker right foot.
Spurs have shown a worrying habit of conceding goals in the final stages of games this season, but this time they held on. Defoe could have doubled the scoreline late on after being put through by substitute Gylfi Sigurdsson, but the striker was denied by Tremmel.
There was late drama as Lloris took out Michu as the Spurs goalkeeper won the ball with a powerful punch, a number of players getting involved in a melee, but the Spaniard was able to continue before referee Mike Dean blew the final whistle.