The victory at the Memorial Stadium moves the Seagulls out of the relegation places in League One.
Striker Andrew connected powerfully with Gary Hart's cross to beat Steve Phillips with a bullet header.
Rickie Lambert shot Rovers ahead with his 28th goal of the season just before the half-hour, but Lloyd Owusu equalised after 43 minutes, sliding in to net another Hart cross.
Brighton had defender Adam Virgo to thank for a brilliant goal-line clearance from Darryl Duffy's 12th-minute shot.
But it was one of few clear chances created by Rovers, who huffed and puffed without forcing many saves from Michel Kuipers.
Brighton's 696 travelling fans celebrated as if they had won promotion at the final whistle, which only brought frustration for the mid-table home side.