Eddie Howe was left frustrated with Bournemouth's lack of "killer instinct" after they lost to 10-man Sunderland.
Things looked bleak for under-pressure David Moyes, who had taken just two points from his first 10 league games in charge, but Jermain Defoe scored from the penalty spot on 74 minutes to steal all three points.
Bournemouth had 22 shots in the match but only registered seven on target as Jack Wilshere and Benik Afobe wasted clear openings late on.
Since scoring six past Hull, Howe's men have now only scored once in their last three league matches.
"We had enough chances," Howe said. "In the last two games we've had gilt-edged chances. We get six against Hull and look free scoring and full of confidence, to creating a hatful of chances and not finishing them off.
"It was a hugely frustrating afternoon. We should have gone 2-0 ahead in the first half, as we had great opportunities.
"They found a way back in it before the red card swung the game in our favour. We had a really good 15-minute spell after that where we battered their goal.
"They couldn't get out of their half and we couldn't capitalise to get that killer touch we needed to win the game."