Murray put the home side ahead from the spot with 18 minutes gone after he had been felled by Mike van der Hoorn and doubled his tally from Jose Izquierdo's 69th-minute cross.
Seagulls boss Chris Hughton was delighted to see his team express themselves in front of goal.
He said, “I thought it was a really good performance. The game certainly opened up in that second-half period, and because of the fact we took the lead, they decided to change [shape], which made it an open game.
“When that happens, one side generally benefits from it and I think we benefitted from it more than they did.
“Offensively, we certainly came onto a decent game. Probably for a side who didn't look like scoring too many goals, that has changed in recent weeks.
“That always has to come on the back of a good team performance - but if you ask the back four and goalkeeper, their disappointment would be that we didn't keep a clean sheet.
“However, I thought we were well worthy of the win, and as the game opened up, we certainly looked like we could score a goal."