A 78th-minute header from Steve Cook proved to be the winner, with Max Gradel and Joshua King scoring the south-coast club's first and second goals respectively.
Swansea twice leveled the game with Modou Barrow — six minutes before the break — and Gylfi Sigurdsson scoring in the 62nd for the Welsh side.
Bournemouth is close to celebrating Premier League survival, as it is now 13 points above the relegation zone in 13th place with just 8 games to play.
Swansea has work to do in 16th place on 33 points.
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