Fraser’s deflected first-half effort settled a curiously low-key game between two distinctly average sides who failed to live up to the glory of the Bank Holiday weather.
The Swans’ fate remains in their hands, with home games to come against relegation rivals Southampton on Tuesday and already-down Stoke on the final day.
The Cherries guaranteed another season of top-flight football with a workmanlike performance which ended a run of three defeats.
Bournemouth started the better but Swansea almost scored from their first attack when a free kick routine worked the ball into Mike van der Hoorn’s path but Bournemouth goalkeeper Asmir Begovic saved brilliantly.
Callum Wilson should then have given the Cherries the lead but sent the ball high, wide and far from handsome when he met Fraser’s perfect cross.
Wilson sent another effort over the bar and, at the other end, Martin Olsson was similarly off target with a header from Andre Ayew’s cross.
Bournemouth finally opened the scoring eight minutes before the break.
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The home fans were cursing referee Kevin Friend when he –rightly – adjudged Alfie Mawson’s foul on Wilson to have been just outside the penalty area.
But they were happy enough moments later when the set-piece was rolled across to Fraser, whose shot took a deflection off Mawson on the way past Lukasz Fabianski.
Jordan Ayew should have equalised soon afterwards. He exchanged passes with brother Andre but sliced his left-foot shot horribly wide.
The Swansea forward at least tested Begovic with a shot in the opening seconds of the second period, then Fabianski tipped a Fraser shot over the bar.
The Swansea ‘keeper should have been helpless when Steve Cook was left unmarked to meet a Josh King cross, but the Cherries defender headed the ball woefully high into the crowd.
Fabianski saved from Nathan Ake but there was nothing doing at the other end for his team, who could not fashion another clear-cut chance.
Swans player of the year Fabianski made a fabulous save to deny Wilson with five minutes to go, but the Cherries striker once more should have done better.
Substitute Lys Mousset went close to sealing the Cherries' dominance of the second half with a late goal.
The Swans now face a crunch clash relegation rivals Southampton on Tuesday night before taking on already-condemned Stoke in the final game next Sunday.
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