The home side, who were without the in-form Junior Stanislas with a calf injury, came closest to scoring in the fifth minute when Hugo Lloris deflected with his legs Charlie Daniels’s close-range shot on to the bar.
Artur Boruc was the busier of the two goalkeepers for most of the match, with Harry Arter personifying AFC Bournemouth's endeavour, although late home pressure resulted in Benik Afobe heading narrowly over.
The point meant Spurs, who are still unbeaten, have 19 points. AFC Bournemouth moved to 10th place.
Man of the Match Harry Arter (AFC Bournemouth)