Northern Ireland international Feeney smashed home a penalty and slid home a late second to give Swansea their fourth away win of the season and leave them top scorers in the division away from home.
Swansea took the lead in the 15th minute through summer signing Ferrie Bodde who curled home a magnificent 25-yard free-kick.
Giant centre-half Dennis Lawrence doubled Swansea's advantage in the 28th minute with a towering header from Thomas Butler's corner.
Former Manchester City striker Lee Bradbury gave Bournemouth hope with a contentious penalty after Lawrence was adjudged to have brought down midfielder Danny Hollands in the area by referee Mike Russell.
Swansea players surrounded the official but he would not change his mind and Bradbury smashed home his first home goal for the Cherries since moving to Dean Court in the summer from Southend United.
Bournemouth went close to grabbing an equaliser in the second half through debutant Adam Lallana.
Lallana, on loan from Southampton, curled a 20-yard free-kick just over the bar after Jo Kuffour had been brought down by Swansea captain Gary Monk.
The Cherries should have equalised in the 65th minute when Lallana and Hollands set up Bradbury who miscued his shot wide and Bournemouth were made to pay for their poor finishing by old boy Feeney.
Referee Russell pointed to the spot after Marc Wilson appeared to handle Lawrence's header from point-blank range and Feeney stepped up to blast the ball home into the bottom right-hand corner.
Feeney grabbed a second goal in the 88th minute with a superb finish. Darren Pratley sent him clear with a long hopeful punt from defence.
Feeney took the ball past Wilson and clipped the ball over Neil Moss in the Bournemouth goal and into the back of the net.