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Andre Villas-Boas's team knew only a victory at White Hart Lane, combined with Arsenal failing to take three points from their visit to Newcastle, would allow them to leapfrog their north London rivals into fourth place in the Premier League on the last day of the season.
But despite Bale's superb long-range goal in stoppage-time following David Vaughan's red card, there was only despair for Spurs as Laurent Koscielny's strike gave Arsenal a 1-0 victory on Tyneside.
That condemned Spurs to fifth place and a berth in the Europa League that will be little consolation after another narrow failure to qualify for Europe's top club competition.
To add to Tottenham's frustration they had their highest-ever Premier League points total, their tally of 72 beating last season's 69, when Harry Redknapp's team finished fourth but failed to qualify for the Champions League because sixth-placed Chelsea won the competition and qualified as holders.
For long periods of this game, it looked as though Tottenham would hand Arsenal the Champions League place as they struggled to find a way past a stubborn Sunderland, whose manager, Paolo Di Canio, had threatened to delay his players' holidays if they did not perform to his satisfaction.
Emmanuel Adebayor had an early chance when he ran onto Kyle Walker's forward header and forced Simon Mignolet to save at his near post, but otherwise neither side was capable of finding an incisive final pass in the opening 20 minutes.
Then Bale charged onto a forward ball from Tom Huddlestone and was wrestled to the ground by Sebastian Larsson.
With the crowd baying for a penalty, referee Andre Marriner instead showed Bale a yellow card for diving, Bale's third this season for the same offence.
And Sunderland almost took a shock lead on the half hour. Danny Graham crossed low from the right and England under-21 forward Conner Wickham met the ball first time six yards out only for Tottenham's France goalkeeper Hugo Lloris to block his shot with an instinctive save.
Spurs were stung into action by that reminder that they had to earn a victory, and Bale nearly did so when his shot from Aaron Lennon's cross cannoned back off Colback. Sunderland captain John O'Shea came almost as close when his headed back-pass nearly crept past his own keeper.
Spurs knew they could not let up in their search for a goal in the second half, but they were dealt two blows in the 52nd minute.
First Carlos Cuellar dived to block a shot by Adebayor with his arm but no penalty was awarded. And almost immediately the Sunderland supporters began to chant the news that Arsenal had taken the lead at Newcastle.
Tottenham still needed to score in case of an Arsenal slip-up, and they tried everything.
Huddlestone volleyed wide, then in the 62nd minute Mignolet fumbled under challenge from Clint Dempsey and was rescued twice by Jack Colback, who blocked Scott Parker's shot then a follow-up from Lennon, this time via a post.
Mignolet redeemed himself with a flying save from a header by Dawson, who was later denied by a third clearance from Colback, then Mignolet blocked another shot from bale.
A rumour then spread that Newcastle had equalised against Arsenal, but it proved unfounded.
Vaughan had been shown a second yellow card for a crude hack at Lennon in the 75th minute.
And Sunderland finally cracked thanks to Player of the Year Bale, who collected a pass from Lennon on the right, darted inside and curled a 25-yard shot over Mignolet and into the top far corner of the net.
Now it was about what Newcastle could do against Arsenal. Unfortunately for Tottenham, the answer was not enough.
