The visitors were on top for much of the first half without seriously threatening, but Vale came back strongly before half-time.
Marc Richards headed Kris Taylor's 36th-minute corner against the crossbar before Louis Dodds' follow up was blocked on the line.
Taylor was himself denied by the woodwork three minutes later when his curling shot from the left edge of the penalty area struck the far post.
Bournemouth stepped up a gear after the break and almost broke the deadlock in the 65th minute when Brett Pitman's glancing header from a Warren Cummings cross bounced back off a post with Chris Martin well beaten.
And in the dying minutes, substitute Steve Fletcher's presence caused confusion in the Vale rearguard and Martin stretched out a boot to deny Pitman a sixth goal in as many games.