The French winger was a constant menace and it was his corner which 29-year-old Murray converted to put Palace in front.
Craig Mackail-Smith might have levelled shortly after half-time but he hit the post when clean through, and Murray made it 2-0 with his 17th goal of the season after being brought down in the area by Tomasz Kuszczak.
The striker, who headed over shortly after, was again fouled in the box in the 71st minute but, after missing two penalties this season when looking for a hat-trick, Garvan took over spot-kick duties and made it 3-0.
Crystal Palace manager Ian Holloway:
"Glenn Murray is a fantastic footballer. His football brain is as good as anybody I have worked with.
"He knows the timing of how to do that run down the middle and his eye for getting on the end of a cross is completely awesome.
"I have had some great players in my time and Glenn is right up there with all of them.
"That's nine goals in six games he has scored for me and that's quite awesome."
Brighton manager Gus Poyet:
"You come here to play a nice game of football against your biggest rival away from home and the least you want is a normal game.
"Going down to 10 so early put a big task ahead of us, but that's football I suppose.
"We came into the game on a good run with plenty of confidence and the team were organised but everything went wrong for two reasons; the sending off and because of the fitness.
"It was an absolutely perfect decision, it was a red card."
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