Bobby Zamora broke the deadlock at Turf Moor after only 58 seconds.
Andre Gray’s penalty was his 11th goal of the season.
The Seagulls extend their own record unbeaten run to 18 league matches.
Albion are now unbeaten in their last 5 games against the Clarets.
Gordon Greer made his 200th league start for the Seagulls on his return to the side.
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