Goals from Max Gradel, Joshua King and Steve Cook proved too much for Swansea as Bournemouth moved up to 13th in the Premier League.
Eddie Howe’s side are now 13 points clear of the bottom three after digging deep at the Vitality Stadium to grab all three points.
Striker King missed two glorious chances inside the first 10 minutes as he blazed the ball over from inside the box on two occasions.
Midfielder Andrew Surman then hit the post in the 14th minute but Swansea also had the chance to score through Federico Fernandez and Gylfi Sigurdsson.
However, Gradel grabbed the opening goal of the game in the 37th minute when he pounced on the edge of the box to drill the ball into the bottom corner.
Bournemouth were only in front for two minutes when winger Modou Barrow went on a mazy run before curling the ball into the bottom corner.
The home side then took the lead again after five minutes of the second half when King found the back of the net after a superb cross from Gradel.
Both teams continued to push forward and the visitors drew level for a second time when Sigurdsson was played in by Leroy Fer. The former Reading man took his time before picking his spot to silence the home crowd.
With the pressure on, Bournemouth found a winner 12 minutes from time as Cook got his second goal of the campaign, as the centre-back stayed onside and nodded home Matt Ritchie’s cross from inside the area.