Antoine Semenya scored the only goal of the game for the Cherries as they leapfrogged their hosts in the standings with four games left of the season.
The game could have ended extremely differently though, with VAR ruling out two Wolves goals, including a last-minute equaliser from Max Kilman due to an offside decision.
Andoni Iraola's men were also forced to see out the closing stages with 10 men, after Milos Kerkez was given his marching orders 11 minutes from time.
The victory for Bournemouth saw them return to winning ways after going three matches without a win following four victories in five.
On the other hand, the defeat for Wolves extended their winless streak to seven matches as they slowly slip down the Premier League table.
Despite Wolves holding the majority of the ball throughout the first half, the visitors were the dominant side as they limited the hosts to very few chances while taking 11 shots of their own.
The first opportunity came just six minutes in when Bournemouth's corner was flicked on at the near post, but the ball looped high and bounced off the crossbar.
Just minutes later and Wolves were almost caught out again as Dominic Solanke was found in the box after Tommy Doyle was caught on the ball, but the striker's effort was eventually blocked.
Wolves did have at least one chance of quality in the first 45, coming in the 13th minute when Pablo Sarabia cut onto his stronger left foot and curled towards the far corner, but Mark Travers was able to turn it around the post as he made his first save of the night.
Jose Sa was called into action multiple times throughout the first half, but his best moment came in the 27th minute when Justin Kluivert was bearing down on goal and attempted to slot into the far corner, but a strong arm from the keeper kept the score level.
Bournemouth finally got what they deserved in the 37th minute as Semenyo robbed the ball in midfield before feeding it to the left, where Milos Kerkez was eventually found rushing into the box with Kilman getting a touch on the full-back's drilled cross, but it fell only as far as Semenyo who smashed home to finish off the move.
That goal signalled a change in tactics from Gary O'Neil, pulling Toti Gomes back into a left-handed centre-back role with Rayan Ait Nouri becoming a left-wing back as they moved into a five at the back.
The visitors should have doubled their lead just before the hour mark when the ball was scrambled inside the box, eventually falling to Marcos Senesi who tried to find the bottom corner but dragged his shot wide.
Wolves thought they had pulled themselves level through Hwang Hee-chan in the 65th minute after he connected with Nelson Semedo's cross to score his first goal of 2024, but a two-minute VAR check found a foul by Matheus Cunha in the build-up resulting in the goal being ruled out.
Bournemouth found themselves down to 10 men in the 80th minute when Kerkez was sent off for a two-footed lunge that caught Matt Doherty heavily on the shin.
The hosts dominated following the dismissal but were unable to truly test Travers with no real chances of quality being created.
That was until the 100th minute when a corner was swung in, with a failed clearance resulting in goalkeeper Sa crossing back into the middle, before being cleared for the second time by Bournemouth.
Boubacar Traore was able to once again put the ball into the middle and find Kilman, who smashed into the bottom corner, but the offside flag went up straight away.
Another two-minute VAR check found Kilman to be offside, ruling the goal out and causing heartbreak for the Wolves fans as the final whistle went just minutes later, resulting in the visitors leapfrogging the hosts and moving into the top 10.