Andy Robinson headed home in the 51st minute, but Joe Partington and Jo Kuffour (90) gave the relegation-threatened Cherries all three points.
The Swans went on the attack from the opening whistle and Robinson had the first strike on goal, but sent his shot high and wide.
The home side dominated the early play, but despite having most of the possession, they rarely threatened the visitors' goal until Tom Butler flashed a 20th minute shot just wide of the post.
Bournemouth won their first corner midway through the half, but the header from Sam Vokes went straight to Dorus de Vries in the home goal.
A minute before the interval a Darren Anderton free-kick was pushed away by de Vries straight to Shaun Cooper, but he sliced his shot well wide.
The Swans took the lead early in the second half when a Butler corner was headed in by an unmarked Robinson.
Swans manager Robert Martinez swapped the ineffective Darryl Duffy for Febian Brandy on the hour as he looked to put the game beyond the struggling visitors.
Bournemouth keeper David Forde then made three superb stops in quick succession as the Swans suddenly found some punch up front.
But the Cherries kept on trying and Vokes and Cooper both had strikes that went close as the home defence backed off.
Darren Pratley should have made the game safe in the 88th minute following a run by Brandy, but he sidefooted wide. Bournemouth broke quickly and Kuffour struck the home crossbar from 25 yards.
In the 89th minute Swansea failed to clear a corner and Partington headed the equaliser.
The Swans were shell-shocked and in the final minute of time added on, Kuffour tapped the ball home to give the Cherries an unlikely victory.