The visitors certainly had the better of the first half, as Antoine Semenyo forced José Sá into an early save, before Marcos Senesi’s header looped onto the top of the crossbar.
Milos Kerkez and Justin Kluivert then forced Sá into two brilliant stops, before Semenyo finally broke the deadlock.
The winger tapped home his eighth goal of the season after a fortunate ricochet off Max Kilman, as Bournemouth went into HT in front.
Wolves’ best chance fell to Pablo Sarabia, who tested Mark Travers with a curling effort, but they were largely second best.
The Cherries threatened to double their lead early in the second half, as Kluivert diverted Senesi’s wayward effort towards goal, forcing Sá into a reaction save.
Semenyo’s strike then deflected just wide, before Senesi found himself free in the box, only to miss the target when he really should have scored.
Wolves thought they had punished him by leveling proceedings soon after, as Hee-chan Hwang headed in Nelson Semedo’s cross, but the goal was disallowed for a foul in the build-up.
The task of taking all three points was made a little harder for Bournemouth when Kerkez was sent off with ten minutes to go, as he lunged recklessly into Matt Doherty without getting the ball.
However, the Cherries managed to hold on for an important win, despite 10 minutes of stoppage time that included Kilman scoring what he thought was a dramatic equaliser deep into injury time, but he was marginally offside and the goal was ruled out.
Victory lifts Bournemouth up to the top-half of the table, while Wolves remain in 12th after a fourth consecutive home defeat.
Flashscore Man of the Match: Antoine Semenyo (AFC Bournemouth)
