Benik Afobe scored on his return to the Bournemouth side as the Cherries left managerless Swansea bottom of the Premier League at the end of 2016.
Afobe's strike sent the away side into an early lead (25) before Ryan Fraser doubled their advantage on the stroke of half-time.
Joshua King came off the bench to end his Premier League goal drought, which stretches back to August, in the 88th minute to seal the win as Eddie Howe's side bounced back from a two-game losing streak and climbed into the top half of the Premier League.
Swansea, who were overseen by caretaker manager Alan Curtis after sacking Bob Bradley on Wednesday, sit four points off safety after sinking to their fourth straight defeat.
Curtis made seven changes to the starting line-up from Bob Bradley's final game in charge, while Howe switched back to his usual 4-2-3-1 formation after back-to-back Premier League defeats.
Fernando Llorente was brought in by Curtis to lead Swansea's attack after his goal against West Ham, but could only direct the home side's best chance wide when he met Naughton's cross in the 22nd minute.
Bournemouth, who dominated the half, made Swansea pay just three minutes later when Afobe, in for King, was on hand to turn in the rebound after Lukasz Fabianski was forced into a quick save from Jordi Amat's skewed clearance.
Jack Wilshere's influence grew as the half went on and after his neat chip set up Junior Stanislas to find the net, which was flagged offside, the on-loan Arsenal player had a hand in the Cherries' second goal.
He slipped through Stanislas once again who, with only the goalkeeper to beat, unselfishly squared the ball to Fraser to score into an empty net.
Stanislas almost made it three 10 minutes after the break after being slipped through by Wilshere but struck wide, before Afobe hit his effort over two minutes later after more good work from the on-loan Arsenal midfielder.
Swansea were forced to bring on Oliver McBurnie for the injured Llorente in the second-half, but the youngster's headed efforts late on did little to test Artur Boruc in goal.
With the home side piling on pressure for a comeback, King raced through from Charlie Daniels' pass to slot beyond Fabianski in the 88th minute to seal it for Bournemouth and leave Swansea a point off Hull at the foot of the table.
Player ratings
Swansea: Fabianski (6), Naughton (6), Mawson (4), Amat (4), Taylor (5), Ki (5), Fer (6), Britton (5), Sigurdsson (6), Dyer (6), Llorente (6)
Subs: Cork (6), Barrow (6), McBurnie (6)
Bournemouth: Boruc (6), Francis (6), Cook (6), Ake (7), Daniels (7), Surman (6), Arter (6), Wilshere (8), Stanislas (8), Fraser (7), Afobe (8)
Subs: Smith (6), King (7), Gosling (n/a)
Man of the match: Jack Wilshere