A brace from Kieffer Moore had given the hosts a 2-0 cushion four minutes into the second half. However, Ryan Sessegnon and Ben Davies helped Spurs draw level before Rodrigo Bentancur netted a dramatic injury time winner.
The Cherries were the better side in the opening half. They put pressure on Antonio Conte's men and deservedly went ahead in the 22nd minute when Moore rounded off a clinical counter-attack.
Moore then doubled the hosts' advantage by powering home a header four minutes into the restart as Bournemouth were seemingly on their way to a huge win.
However, Spurs mounted a terrific comeback, including a 92nd-minute winner from substitute Rodrigo Bentancur to seal all three points.
With 26 points from 13 games, Tottenham remain in third place in the Premier League standings, while Bournemouth slip to 14th after a third straight loss.
On that note, here'rethe player ratings for Tottenham Hotspur:
Hugo Lloris - 6.5/10
The Tottenham custodian conceded twice to Moore but made two important saves, including a good one against Marcus Tavernier.
Davinson Sanchez - 6/10
He was sloppy in defence and was at fault for Bournemouth's second goal, allowing Moore to power home a header.
Clement Lenglet - 7/10
The former Barcelona man struggled to cope with Bournemouth's press early on but improved as the game wore on. Lenglet made some good recoveries and was strong in the air.
Ben Davies - 7.5/10
The Welshman got forward well and headed home the equaliser from close range.
Emerson Royal - 6/10
Emerson was beaten by Moore for Bournemouth's second, and his crosses didn't come through either.
Oliver Skipp - 6.5/10
He looked to make things happen with promising runs down the wings. Skipp forced a save from Travers, but his crosses were wayward, and he was taken off at the break.
Yves Bissouma - 6/10
He burst forward on a couple of occasions in the first half to link up with his forwards, but nothing meaningful came off them.
Pierre-Emile Hojbjerg - 7/10
Hojbjerg set up Sessegnon with a clinical slide-rule pass andhad the chance to score one himself but fired his effort over the bar.
Ryan Sessegnon - 7.5/10
The 22-year-old triggered Spurs' comeback with a well-taken goal just before the hour mark and played a key role in winning back possession.
Harry Kane - 6.5/10
The Tottenham striker improved after the break and got more involved in the proceedings. Kane, though, went into the books for tripping over Jefferson Lerma.
Heung-min Son - 6.5/10
It was another goalless endeavour for the Korean talisman, but his corner deliveries were sharp and accurate.
Ratings of Tottenham Hotspur Substitutes
Lucas Moura (46' for Skipp) - 6/10
He went forward to help out offensively, but his crosses were largely inaccurate.
Eric Dier (58' for Sanchez) - 6.5/10
The midfielder had a shot blocked from a corner.
Rodrigo Bentancur (58' for Bissouma) - 7/10
He had an effort blocked but scored on the rebound to complete the turnaround.
Ivan Perisic (64' for Royal) - 7/10
The Croatian added immense threat after coming on and assisted Davies for Spurs' equaliser.
Bryan Gil (84' for Sessegnon) - N/A
Gil was barely seen after coming on.