But the visitors also had to thank goalkeeper Michel Kuipers who made fine saves to deny David Pipe, Byron Anthony and young substitute Charlie Clough in Saturday's League One clash.
Westlake pounced to net in a goalmouth scramble after 71 minutes and five minutes later Murray made sure of the points by heading in a deep cross from Dean Cox.
Rovers were awful in the first half, but looked to be getting on top when Clough made his debut as a 67th-minute substitute for Sean Rigg.
Kuipers performed heroics to keep Brighton level before the two goals completely knocked the stuffing out of the home side.
Substitute Andy Williams forced another good save from Kuipers, but it was a miserable last game at the Memorial Stadium for Rovers before ground redevelopment as Brighton were no more than workmanlike, but showed greater composure in front of goal.