Albion lead the old enemy 1-0 in this FA Cup third round match in front of a thin crowd.
Dale Stephens put the Seagulls ahead after 25 minutes after good work by Ezequiel Schelotto.
Stephens fired home with Palace keeper Wayne Hennessey only able to parry the ball into the net.
Izzy Brown was injured in a challenge by Jeff Schlupp in the opening minutes.
Both men went off, with Brown replaced by Sam Baldock. Pape Souare replaced Schlupp.
Tim Krul in the Albion goal has had little to do – with one scare as the ball was played across the penalty area by Andros Townsend.
Uwe Hünemeier had to steer the ball wide.
Albion are just 45 minutes away from a tantalising fourth round tie at Middlesbrough.