The Seagulls took the lead six minutes in when Murray notched his 14th goal of the season from close range.
Murray could have added a second in the 14th minute but his shot was saved by Luke Daniels.
But the hosts were two up on the half-hour mark, Seb Carole crossing for skipper Andrew Crofts to score with a neat finish.
Substitute Ashley Barnes, making his Seagulls debut after his loan move from Plymouth, added the third with nine minutes remaining in some style with a drive from 25 yards.
By that time Rovers had been reduced to 10 men after Andy Robinson was dismissed on his debut for a challenge on Inigo Calderon.