The Seagulls suffered a second-minute shock when Will Hoskins fired Rovers ahead from 25 yards, but a rasping drive from Ashley Barnes gave Gus Poyet's side a 38th-minute equaliser.
Elliott Bennett then slotted home from a Barnes pass after 51 minutes, then a 74th-minute own goal from Cian Bolger and a 78th-minute header from Glenn Murray from Craig Noone's cross put the visitors in command.
Bolger then set up Hoskins to score his second of the game to take his goal tally for the season to 17, but the damage had already been done.
Rovers hit a post through a long-range effort from Gavin Williams and had another Hoskins strike ruled out for a marginal offside decision.
But Brighton showed plenty of quality throughout the game and had the ball in the net twice more themselves only to be denied by a linesman's flag.