Eddie Howe's Cherries took the lead in the 25th minute with Afobe scoring from close range on the rebound after Jordi Amat narrowly avoided deflecting the ball into his own net.
Fraser raced into the area in stoppage-time at the end of the half to smash in a Junior Stanislas cross, doubling the visitors' lead.
Swansea, under caretaker manager Alan Curtis, struggled to gain possession throughout the second half, before Bournemouth substitute Joshua King shot past goalkeeper Lukasz Fabianski to seal the win.
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(Reporting by Hugh Lawson, editing by Ed Osmond)
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