The pair were on target either side of half-time in front of a crowd of 25,759 at the Amex Stadium, as the Tykes - under the guidance of caretaker boss Micky Mellon - forged ahead in their first Sky Bet Championship match since the weekend dismissal of David Flitcroft.
Matthew Upson got the hosts back in it by halving the deficit just after the hour mark, but they could not find an equaliser.
The Seagulls, who went into the game boasting a six-match unbeaten run, settled quickly and Spanish midfielder David Lopez drove wide before a dangerous cross from Welshman Andrew Crofts was cleared by skipper Martin Crainey.
Lopez did well to whip in a pacey cross in the 17th minute and Peter Ramage kept his cool to clear under pressure.
Winger Craig Conway came close to giving Brighton the lead by capping a surging run with a fierce shot from the edge of the area which goalkeeper Jack Butland did well to push onto the crossbar.
Barnsley, without a goal in 290 minutes heading into the game, looked threatening in the 25th minute when Polish midfielder Tomasz Cywka broke into the area and his goalbound shot was blocked by Spanish defender Bruno Saltor.
Referee James Linington handed out his first yellow card when Ramage chopped down the on-rushing Conway, and Barnsley midfielder Mellis was later off target when he tried his luck from 25 yards.
The Seagulls were shaken when Northern Ireland international McCourt struck to end Barnsley's goal drought.
McCourt broke strongly through the middle and, after playing a one-two with Marcus Tudgay, beat goalkeeper Tomasz Kuszczak with a close-range shot which the Pole got a hand to but could not keep out.
Brighton ended the first half in frustrating fashion as Barnsley pushed forward with McCourt and David Perkins linking up intelligently.
Barnsley doubled their advantage five mintues after the break with a superbly worked goal from Mellis, who latched onto a smart low pass from Tudgay to net from close in.
Mellis timed his run to perfection and, although Kuszczak managed to get a hand to the ball, he could not prevent it from sailing into the roof of the net.
Barnsley broke with pace on the hour and Kelvin Etuhu put a shot over the bar as the visitors continued to play with confidence.
Former England defender Upson struck to put Brighton back in the game by rising unchallenged to head home a corner from Conway in the 62nd minute.
Referee Linington was forced off injured 20 minutes from time to be replaced by fourth official Charles Breakspear.
Substitute Kemy Agustien crossed dangerously for Brighton and striker Ashley Barnes, with three goals in his previous three games, put a close-range header over with only Butland to beat.
Brighton dominated the closing stages and substitute Leroy Lita had a shot blocked before Butland brilliantly denied Will Buckley.