The Cherries were hanging on grimly to the win which would have edged them a step closer to safety from relegation when Alan Tate, a second-half substitute, chose the perfect moment to score his first League goal of the season.
Bournemouth failed to clear a corner and Tate smashed a 25-yard left-foot volley into the roof of the net.
Rattled Bournemouth were clearly going to struggle to hold on to their lead and Swansea levelled with three minutes remaining.
Neil Moss made an outstanding save to block a shot from another Swansea substitute, Pawel Abbott, but the rebound fell into the path of Lee Trundle who scored from six yards for his 17th of the season.
It left Kevin Bond's side with a further seven minutes of normal and stoppage to survive and there were some anxious moments before referee Clive Penton finally blew his whistle.
All this was in contrast to the first hour which Bournemouth dominated as they were led by an outstanding midfield display from their experienced former England international Darren Anderton.
Bournemouth deserved their 22nd minute lead when Anderton took a corner from the right and Marc Wilson rose unchallenged to score with a header.
Anderton, and then Luke Summerfield, went close to adding further goals before the second arrived on the hour.
Wilson and James Hayter combined in a sweeping move that allowed David McGoldrick to score with a low right-foot shot.
It was McGoldrick's sixth goal in 11 starts since arriving on loan from neighbouring Southampton.
But when Anderton went off in the 63rd minute, visibly tired, Bournemouth were never the same force and it was no surprise when Tate hammered in Swansea's first to set up an exciting finish.