Substitute Michael Gray made it 3-0 before the home side pulled a goal back from Andy Robinson's free-kick.
Matt Derbyshire made it 4-1 to Rovers late on.
Swansea: Gueret (Murphy 79 mins), Ricketts (Anderson 79 mins), Austin (Tate 46 mins), Monk (Tudor Jones 63 mins), Martinez (Robinson 79 mins), Britton, O'Leary, Trundle, Forbes, Goodfellow (McLeod 46 mins), Iriekpen. Subs not used: Connor, Gurney.
Rovers: Friedel, Neill, Matteo (Gray 70 mins), Todd, Mokoena (McEveley 75 mins), Reid (Taylor 80 mins), Emerton (Douglas 73 mins), Savage (Tugay 46 mins), Kuqi (Derbyshire 63 mins), Gallagher (Gresko 70 mins), Pedersen (Flitcroft 63 mins). Sub not used: Drench.