The former Arsenal man found the net in either half, although his first will officially go down as an own goal as it took a telling touch off Swansea defender Alfie Mawson on its way past Lukasz Fabianski.
Bournemouth have now won back-to-back games in the Premier League for the first time in a year, while successive defeats for a well-below-par Swans side leaves them three points above the dropzone heading into the two-week international break.
Fraser turned provider soon after, sending in a fine delivery for matchwinner Afobe to nod wide from just a few yards out after holding off his man.
Bournemouth got the luck they required, however, as soon after Joshua King's flick-on evaded his own goal by a matter of inches, Afobe saw his deflected shot from the edge of the box take a nick off Mawson and creep over the line.
Sigurdsson, with a league-high 11 assists to his name this term, led the Swansea charge for a response by sending a dipping shot towards the far corner.
Artur Boruc was equal to it on that occasion, helping the ball past the post with his fingertips, while Adam Smith's free kick right down the middle was the closest the Cherries came to doubling their tally in the first half.
Swansea, who have only once before recovered from behind at half time to win a Premier League game, were doing little to force their way back into the contest in the early throes of the second period.
Some slack play was punished on a few occasions, the most costly of which nearly saw Dan Gosling pick out the bottom corner if not for a smart stop from Fabianski down to his right.
Fraser was the next to capitalise on the high press paying off, also testing Fabianski with a routine stop, with Swansea taking until the hour mark before finally stepping things up.
The Welsh outfit were unable to create any real clear openings, though, and that came back to haunt them as the home side added a second 72 minutes in through another Afobe strike.
There was no doubt that this one belonged to the forward, sweeping the ball into the far corner via the post after being slipped through by last weekend's hat-trick hero King.
Fabianski had to be alert to prevent King adding a third in the final 10 minutes, reacting quickly to scoop the ball behind after the Norway international leapt high to meet substitute Jack Wilshere's cross.
Wilshere was the next to be thwarted by Fabianski late on, but Bournemouth had already done more than enough to earn the points, seeing them move nine clear of danger and surely safe for another season.