Ryan Fraser's effort was enough to see off the 'Swans', although Lucasz Fabianski did well to keep the score at 1-0.
Bournemouth however have confirmed their safety for the following season, their third consecutive in the top flight.
Swansea will drop into the relegation zone should Southampton gain a point or more away at Everton in Saturday's late game, and their next fixture: Southampton at home on Tuesday.
It appears that the race to avoid the final relegation spot will hinge on the outcome of that game, but the 'Swans' are on a seven game winless run that shows no signs of improving.