Third-placed Spurs would have secured Champions League qualification for next season with victory, but they were brilliantly denied on numerous occasions by 19-year-old debutant Mark Travers in the Cherries goal before spectacularly losing their cool.
Son Heung-min was sent off just before the break, having returned from the suspension that kept him out of the midweek European semi-final first-leg defeat to Ajax, and Juan Foyth – introduced as a half-time replacement – was also trudging down the tunnel just two minutes and 13 seconds after the restart.
And after keeping Bournemouth at bay for the majority of the second half, Spurs allowed Nathan Ake to nod in the winner in the first minute of stoppage time.
Mauricio Pochettino's men may now require a result against Everton four days after a trip to Amsterdam as their involvement in the Champions League both this season and next remains uncertain.
Travers quickly found his feet with a string of superb saves, turning away a powerful drive and a testing header from Dele Alli, as well as twice denying Lucas Moura as he exploited space behind a haphazard Bournemouth back line.
But an incredibly one-sided contest took a turn on the stroke of half-time as Son saw red.
Referee Craig Pawson had earlier turned down a pair of Bournemouth penalty appeals and generously opted against showing Eric Dier a second yellow card, but Son was dismissed as he shoved Jefferson Lerma to the floor.
Foyth and Victor Wanyama were introduced at the break as Pochettino took no risks with Dier and Toby Alderweireld, also cautioned, yet the substitute defender soon lunged in on Jack Simpson and Spurs were reduced to nine men.
Bournemouth looked as though they would be frustrated by a resolute Tottenham defence, but Ake powered in a header from Ryan Fraser's corner to land another blow to Pochettino's men.
