The result meant we took advantage of Chelsea's defeat at Southampton to climb up to third in the table with seven matches remaining.
It was a case of lightning striking twice for Vertonghen, who scored the only goal of the game when the teams met at White Hart Lane in December.
His goal at the Liberty Stadium was just as good - and equally important - as we recorded a ninth away win of the campaign so far, bettered only by Manchester United.
Vertonghen and Bale combined for both goals in the seventh and 21st minutes.
Swansea pulled a goal back in the 71st minute through Michu and cranked up the pressure without seriously testing Brad Friedel again.
Andre Villas-Boas made three changes from the 1-0 loss against Fulham on March 17.
Brad Friedel was in goal for Hugo Lloris, who was out with a slight knee problem. Aaron Lennon, who missed the Fulham game through injury, returned for Benoit Assou-Ekotto while Kyle Walker returned for Steven Caulker.
Michael Dawson was fit to start after being forced off at half-time against Fulham. Young goalkeeper Jordan Archer, recalled from his loan spell at Wycombe, took his place on the bench.
We started well and grabbed a key early goal on seven minutes. Vertonghen carried the ball out of defence and slid into Bale, continued his run forward collected Bale's return in the box, controlled and touched home past Michel Vorm.
We took control for the next 10 minutes. Mousa Dembele released Emmanuel Adebayor on goal but having raced away from Ashley Williams, the striker was denied one-on-one by Vorm.
Michu headed Swansea's first serious sight at goal wide from Dwight Tiendalli's corner on 20 minutes but it was soon 2-0.
Swansea made a bit of a mess of it playing out from the back and the ball ended up at Vertonghen's feet on half-way. He fizzed a pass into Bale, who controlled and fired into the top corner without hesitation from 20 yards, a great strike.
The second goal sparked Swansea into life. Nathan Dyer lofted a chance just wide and Friedel needed to be alert to palm out Tiendalli's fierce effort from the right angle.
Bale shot just wide on the half-hour but the home side must have been wondering how they failed to reduce arrears five minutes later when Dyer met Tiendalli's cross six yards out. His header crashed back off the crossbar, struck the same player and went out for a goal-kick.
Friedel had to be alert to block from Michu after Dyer's quick free-kick at the start of the second half.
There were chances at both ends. Vorm did well to tip away Gylfi Sigurdsson's curler before Michu powered a header wide from 12 yards.
The next goal was always going to decide the nature of the final period and Swansea found their response through Michu, a firm header in off the post from Tiendalli's corner.
The home team cranked up the pressure but it was Bale who almost struck next after racing away for fully 70 yards, his low shot hit the foot of the near post.
Vorm was tested again with five minutes remaining, the save of the game low down to his right from substitute Jermain Defoe.
Swansea's best chance to equalise was actually thwarted by Bale sliding in the way of Dyer from close range and it was Bale who had the final effort in five minutes of injury time, another lighting break that ended with a shot straight at Vorm.
Spurs (4-4-2): Friedel; Walker, Dawson, Vertonghen, Naughton; Lennon, Dembele, Parker, Sigurdsson (Holtby, 76); Adebayor (Defoe, 61), Bale. Unused subs: Archer, Assou-Ekotto, Caulker, Huddlestone, Livermore.
Swansea: Vorm, Flores (Monk, 66), Williams, Britton, Michu, Hernandez (Shechter, 79), Dyer, Routledge, de Guzman (Ki Sung-Young, 57), Tiendalli, Davies. Unused subs: Tremmel, Bartley, Lamah, Moore.
Yellow cards: Swansea - Michu, Davies. Spurs - Adebayor, Holtby, Parker, Walker.
Goals: Swansea - Michu (71). Spurs - Vertonghen (7), Bale (21),
Referee: Mr A Taylor.
The lads bounced back from successive defeats in the Premier League with a performance that showed both sides of the team's character - flowing football to forge 2-0 ahead in the first half, no little grit defensively to see the game out after Swansea pulled a goal back with 20 minutes remaining.