The 32-year-old striker, on a season-long loan from Bournemouth and in his second spell at Albion, has now scored five goals this season - all of them coming at the Amex Stadium.
The victory takes the Seagulls above Barnsley, who lost for the second game running having gone down 2-1 at home to Reading last weekend.
Murray, recalled in place of Jamie Murphy as Chris Hughton’s only change to his league side, came close to putting the Seagulls ahead in only the second minute.
Murray’s goalbound shot was deflected over the bar by keeper Adam Davies, the ball coming off the head of the former Sheffield Wednesday man.
Barnsley defender Cole Kpekawa then shot narrowly wide of David Stockdale’s left-hand post from 30 yards.
The Seagulls broke the deadlock with a sweeping counter-attack move which saw Murray hit his fourth of the season.
Murray fired home left-footed from 12 yards after French winger Anthony Knockaert had fed the ball to Beram Kayal.
Murray should have increased the lead midway through the half when he stabbed the ball wide from only six yards after Knockaert had combined with Gaetan Bong.
Barnsley wasted a glorious opportunity to level 10 minutes before the interval when, following a short free-kick, Sam Winnall wastefully headed wide from seven yards after a cross from Adam Hammill.
Barnsley keeper Davies then came to his side’s rescue by turning the ball behind for a corner after Knockaert’s shot had deflected off Winnall.
The Seagulls doubled their advantage three minutes after the break when Murray headed home from just outside the six-yard box following a free-kick from Czech winger Jiri Skalak.
Murray was well-placed again five minutes later, but Davies smothered his shot from Skalak’s cross.
Striker Adam Armstrong, on loan from Newcastle, headed a rare chance for Barnsley wide after a centre from Marley Watkins.
Centre-half Shane Duffy, Brighton’s record signing from Blackburn, should have tested keeper Davies when heading wide from Knockaert’s free-kick.
Albion keeper David Stockdale had little to do throughout but pulled off a terrific save 15 minutes from time to keep out a goalbound shot from Josh Scowen.
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