Tottenham's task was made all the more hard two minutes before the interval when forward Son Heung-min was sent off for pushing Jefferson Lerma and halftime substitute Juan Foyth lasted 125 seconds before seeing red for a lunging tackle.
In truth, they should have been winning going into the second half.
Bournemouth struggled to make their numerical advantage count until Nathan Ake climbed highest to meet a corner and head a dramatic victor in the 90th minute.
Tottenham still have work to do in the race to finish in the Premier League's top four after their nine men lost 1-0 late on at Bournemouth on Saturday.
The game started evenly but nearly saw Spurs go ahead in stunning fashion.
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.
Bournemouth had plenty of the ball but they struggled to make their two-man advantage count as they rarely troubled Hugo Lloris.
Travers had an excellent first-half, denying Dele Ali spectacularly, as well as making two great saves from two Lucas Moura efforts. "Huge potential, we think this is an ideal game for him to show what he is capable of".
Things went from bad to nightmare territory for Spurs two minutes after the break, when Foyth - who had just entered at the start of the second half - cut down home defender Jack Simpson with a high boot.
It was a moment of madness and his red card was deserved.
Spurs switched to a 4-3-1 formation after the second sending off, as they stayed compact and battled to try and keep hold of the ball whenever they could.