Albion's manager hailed the performance from his forward.
Brighton & Hove Albion manager Chris Hughton praised his two-goal match-winner Glenn Murray, as the striker returned to the starting line-up and his double completed a third straight Championship win for the Seagulls.
Murray scored in each half, the first a classic counter-attacking move, followed by a text-book Murray header from a Jiri Skalak free kick.
Hughton said, "Before today, he'd got three goals for us inside the first three games, but today was his best all-round performance.
"Not only the goals he scored, but he led the line really well. He had a frustrating time last season, and sometimes it just takes that little bit of time to get back to your best level.
"The first goal was a classic counter-attacking goal, and when the ball went to Beram [Kayal], I felt he should have finished it, but he laid it off to Glenn, which proved a right decision."
LATEST NEWS FROM SEAGULLS.CO.UK
- REPORT: ALBION 2 BARNSLEY 0
- NEW DEAL FOR DUNK
- DUFFY NAMED IN IRELAND SQUAD
- ALBION AND AMEX JOINTLY SPONSOR SNOWDOG SCULPTURE
- GALLERY: READING
Hughton felt that Albion should have taken other opportunities to extend their lead, before Murray's glancing header doubled the advantage.
He added, "The two goals were very good, but probably the only disappointment was that we could have made the game more comfortable for ourselves.
"I wanted us to build on the first goal, and we probably made it a little harder work than we should have done, but there was some really good play, and opportunities.
"I'm a little bit frustrated that we didn’t make it easier for ourselves, but it's another win and, of course, another clean sheet as well.
"We had some good chances in the first half; Barnsley are a team in good form, and for periods of the game they showed why."
The result also meant a third successive clean sheet in the Championship, since Albion's home defeat to Brentford.
"We had to defend well at times, they were a threat and will certainly score goals in many of their games this season, so I’m really pleased with the clean sheet.
"We had that difficult period where we lost two games, one up at Newcastle, and the Brentford game, which was the really disappointing one. But since then, our league form has been really good."
Tweets by @OfficialBHAFC