Spurs ended a winless run of five league games with a good performance against the Welsh side, with Bale and Van Der Vaart also finding their top form once more
First blood went to the home side when Rafael van der Vaart converted after good work from Gareth Bale, but the Welsh outfit hit back after the break with another fine goal, this time from Gylfi Sigurdsson.
But the hosts re-gained their lead after scorer turned provider when Adebayor headed home from Van Der Vaart's corner. The former Gunner then nodded past Vorm again to put Harry Redknapp's men on par with his former club.
Redknapp made four changes to the side that beat Bolton in their FA Cup replay on Tuesday, with Brad Friedel, William Gallas, Younes Kaboul and Sandro coming back into the starting line-up. Aaron Lennon was back from a hamstring problem and started on the bench.
As for the visitors, Brendan Rodgers replaced Steven Caulker, who was ineligible to face his parent club, with Garry Monk in his only change to the team which tasted defeat against Everton last weekend.
The opening quarter of an hour included a flurry of chances for each side, firstly Van Der Vaart shooting wide after Emmanuel Adebayor knocked back Luka Modric's neat cross.
Then the visitors went close through former Spurs midfielder Wayne Routledge, the 26-year-old's snap-shot just missing the left upright.
Adebayor was the next to miss the target. Bale was allowed space to stretch his legs on the left flank and proceeded to whip the ball across the face of the box. However, the Togolese frontman couldn't direct the ball goalwards after sliding in at the near post.
Back at the other end, Swans full-back Neil Taylor had a arguable shout for a penalty waved away. The Welshman got goal-side of William Gallas, who then attempted to pull back the opposing defender - nothing was given, and in truth there were minimal appeals, as Taylor got his cross away, which was nearly deflected past Friedel.
The hosts did finally bag the opener just inside the 20 minute mark, through Van Der Vaart.
Bale, who had been enjoying a lot of space on the left flank, again ran free on the wing before putting the ball into the box. Ashley Williams attempted to clear but ended up putting it on a plate for the Dutchman to calmly slot home with a curling finish.
Tottenham were more reserved than expected, and prioritised staying solid in defence. The north London side pressed their traveling opponents each time they lost possession, Scott Parker putting a good shift in as he broke up a number of Swansea attacks.
Van Der Vaart remained an influential man for Spurs and half an hour in they went close when his corner was met with an almighty header from Kaboul. The defender was a fair distance out but the effort needed Michel Vorm to move quickly before parrying away.
Redknapp's men continued to search for a second goal before the break, and it was Bale who went the closest after swinging a boot at Modric's knock down from Benoit Assou-Ekotto's ball in, but it rose over the bar. The Croatian playmaker later wasted a chance of his own when he decided to shoot instead of threading Adebayor in.
Throughout the half Swansea managed to put together some neat passing, with Scott Sinclair showing moments of class. However, the former Chelsea man was crowded out and fouled early by the home side in a successful attempt to stop the Swans from getting into their flow.
Shortly after the break, Sigurdsson forced Friedel into making an outstanding save. The Swans midfielder turned sharply before producing a left-footed strike that the American showed great agility to tip onto the post.
Apart from that chance there was little action for the first 15 minutes of the second period, both sides largely cancelling each other out as they did for most of the opening half.
However, just before the hour mark Sigurdsson, who had scored five in his last four away games before the clash at White Hart Lane, added to his season's tally.
The ball fell to the Iceland international after good hold-up play by Routledge and he made no mistake, firing a delightful half-volley from outside the area past the scrambling Spurs keeper.
Spurs looked for a speedy return and went close six minutes after the equaliser. Bale again caused trouble on the left touchline and delivered a dangerous ball into the middle, Van der Vaart beat his man and managed to direct a powerful header towards goal, only to be denied by a good near-post save from Vorm.
Bale and Adebayor also tested the the Swans keeper soon after, but both failed to get good enough connections to pose any real threat to the Dutchman's goal.
The hosts were looking the more likely to score again, and if it was not for a crucial interception from Williams, after a driven low cross from Bale, Adebayor would have found a second.
However, the Togo forward did not have to wait long to ripple to net. With just over a quarter of an hour left on the clock Adebayor rose above the pack to head Van Der Vaart's corner past a helpless Vorm.
In truth there were little signs of reply from Swansea, with the credit for that going to a solid display from Redknapp's men.
Spurs went on to see out the game comfortably and even had time to grab a third.
Bale, who looked fantastic all day, ran at the defence before playing Lennon in down the right flank. The Englishman then crossed for Adebayor to find the net with his second headed goal, securing the points with under five minutes left to play.