In what was an even first half at the Vitality Stadium, the hosts broke the deadlock on the half hour mark thanks to an Alfie Mawson own goal and a bit of luck.
Joshua King found Benik Afobe whose subsequent attempt on goal was slightly scuffed but deflected off Mawson to leave Lukasz Fabianski with no chance.
Afobe was on form throughout the match and if the first goal was not credited to him then the second effort certainly was, with the Cherries striker doubling the lead on 72 minutes.
After receiving the ball from King, Afobe evaded a Swansea defender to then slide the ball into the bottom corner to effectively seal the game.
Swansea did have a couple of good opportunities, as Gylfi Sigurdsson forced a great save from Artur Boruc on 36 minutes and King nearly put the ball into his own net ten minutes earlier, but the Swans found genuine chances hard to come by, with Fernando Llorente especially quiet.
Bournemouth had moments to add to their tally including, on 79 minutes, when Lukasz Fabianski pulled off a lightening reaction save from a powerful King header to spare the visitors an even bigger deficit.
Swansea have now lost four away matches in a row and fall further into the relegation battle while Bournemouth's important win provides them some much-needed breathing space heading into the international break.