Spurs needed to win to stand any chance of qualifying for the UEFA Champions League but it looked like they would be frustrated until Bale rounded off a wonderful individual campaign with another special strike in the 90th minute.
However, Arsenal's victory at Newcastle United ensured that Tottenham would have to settle for a fifth-place finish despite a record points haul in the Premier League.
The margin of Spurs' victory could have been more convincing had they been granted any of several penalty appeals, while Sunderland also defended doggedly and Simon Mignolet pulled off a series of fine saves.
The onus was on Tottenham to take the attack to a Sunderland side whose Premier League survival had been guaranteed by Wigan Athletic's loss to Arsenal, and the first half was dominated by the hosts at White Hart Lane without reward.
It looked like the breakthrough would come in the 21st minute when Bale was sent tumbling in the area by a push from Sebastian Larsson, but instead of giving a penalty referee Andre Marriner felt that the Welshman had dived and issued a yellow card which sparked a furious reaction from the player and the crowd.
Spurs had another appeal for a spot-kick waved away when Bale's shot from close range crashed into the arm of Jack Colback, while Mignolet made decent saves from Emmanuel Adebayor, Tom Huddlestone and a Bale free-kick.
Sunderland were disciplined in defence but only broke forward sporadically, with Hugo Lloris showing quick reflexes at his near post to repel a close-range flick from Connor Wickham.
Lloris again had to be alert to pull off a fine save down to his left from Danny Graham at the start of the second half after lazy play from Huddlestone in midfield had allowed Sunderland to pinch the ball.
Tottenham then had another shout for a penalty waved away by the referee when Carlos Cuellar looked to handle Adebayor's shot as he slipped to the floor, and the feeling of frustration grew as news filtered through of Arsenal's lead against Newcastle.
Colback made two goal-line clearances to deny Scott Parker and then Aaron Lennon in quick succession, and a number of chances came and went as Mignolet continued to impress and Sunderland's whole team worked hard.
The Black Cats were reduced to ten men in the 75th minute, however, when David Vaughan was shown a red card for a second bookable offence.
Spurs finally netted the goal they deserved when Bale cut back inside 25 yards from goal and fizzed a spectacular, curling shot past a despairing Mignolet and into the top corner.
The final few moments were spent with the fans desperately wishing to hear that Newcastle had pegged back Arsenal, and when that news never materialised it left the taste of victory very bittersweet.