That was our 19th effort on goal - the final tally was 24-4 in our favour - in a match we dominated thanks in main to a work ethic that simply refused to allow the visitors to settle into their renowned passing game.
The result made it four wins in our last five matches and moved us back up to fourth place in the Premier League, level on points with Chelsea.
And there was an added bonus as Scott Parker made his return with a late appearance off the bench - his first action this season after recovering from an Achilles injury.
Andre Villas-Boas made just one change from last week's loss at Everton as Kyle Naughton came in for Steven Caulker. He started at left-back as Vertonghen switched to partner William Gallas centrally.
We pressed high up the pitch throughout and that pressure led to our first three chances - all carved out from hustling Swansea players off the ball.
The first saw Emmanuel Adebayor's pass send Jermain Defoe slightly wide before cutting onto his right foot and shooting straight at Gerhard Tremmel.
Mousa Dembele was next to win the ball and then showed great awareness to backheel for Defoe but Michu, of all players, was there to make a goal-saving block.
Seconds later and Kyle Walker won the ball back, got down the byline and crossed low for Adebayor, but this time Chico Flores got in the way.
Defoe and Clint Dempsey tried their luck before Aaron Lennon played a one-two with Walker and tried to set-up Defoe, but Ashley Williams read the pass and cleared.
Walker then unleashed a thunderbolt that might well of taken the net off had Tremmel not been in the way.
Swansea, happy to drop nine players behind the ball when we were in possession, then caught us on the break as Wayne Routledge released Jonathan De Guzman, who fired just over.
Lennon's low strike was well taken by Tremmel down to his right in the 41st minute and the half ended with Michu going for a spectacular effort from half-way after a mix-up between Dembele and Gallas, his effort close enough for a bit of discomfort, but always sailing over.
Swansea had the first chance of the second and their best of the match as Routledge crossed from the left and Nathan Dyer, six yards out, failed to connect with a header.
Adebayor took off from halfway on 50 minutes, striding away to the edge of the box where his low shot was palmed away by Tremmel.
The next chance arrived on 59 minutes, started by Sandro's challenge on the edge of our box. Lennon sprinted away and Defoe rolled the ball into the path of Walker, who blazed wide.
It was a real chess game when we were in possession, trying to find the gaps. Dembele won the ball and found Defoe 20 yards out, this time the striker's low effort curled just wide.
Gylfi Sigurdsson entered the action for Dempsey in the 69th minute and we were soon forced into a second change as Adebayor limped off, replaced by Andros Townsend.
Townsend played his part in the winner as he was upended on the right touchline. Walker swung in the free-kick from the right, it glanced off Michu's head and Vertonghen was there to finish.
The Belgian international was involved in everything in the next minutes, glancing Walker's corner wide and then striking a free-kick that clipped off the wall and flew just wide.
Sigurdsson sent Defoe clear one-on-one but Tremmel saved with is legs.
Five minutes added time were negotiated safely thanks to two huge punches clear from Hugo Lloris, the second setting up the final chance, Townsend denied one-on-one on the break.
Spurs (4-4-2): Lloris; Walker, Gallas, Vertonghen, Naughton; Lennon, Dembele (Parker, 90+3), Sandro, Dempsey (Sigurdsson, 69); Adebayor (Townsend, 72), Defoe. Unused subs: Friedel, Caulker, Huddlestone, Livermore.
Swansea (4-2-3-1): Tremmel; Tiendalli, Flores, Williams, Davies; Britton, Ki Sung-Yueng (Moore, 75); Dyer (Graham, 87), De Guzman (Augustien, 60), Routledge; Michu. Unused subs: Cornell, Monk, Shechter, Richards.
Yellow cards: Spurs - Dembele, Defoe, Livermore. Swansea - De Guzman, Flores.
Goals: Spurs - Vertonghen (75).
Referee: Mr M Dean.
The finish was worthy of winning any game as the centre-back swept home Kyle Walker's free-kick on the half-volley with his right foot from 12 yards.