Argentinian forward Emanuel Villa netted a hat-trick as Derby set up a Carling Cup fourth-round home date with Leeds following a 4-1 victory on the south coast.
The Rams, who have now lost just one of their last 12 games, took the lead in the 28th minute.
Poland striker Przemyslaw Kazmierczak, on loan from Porto, delivered a cross which Albion goalkeeper John Sullivan came to collect. But under pressure, he dropped the ball and Villa - who went from villain to hero after scoring at both ends in the East Midlands derby against Nottingham Forest on Sunday - was on hand to prod home from six yards.
The Rams doubled their advantage six minutes later when Nathan Ellington slotted past Sullivan after Dean Leacock's ball had put him clean through. But Brighton responded immediately and cut the deficit within two minutes when Tommy Elphick headed home Kevin Thornton's corner.
However, Villa put the result beyond doubt in the 73rd minute, heading home a cross from substitute Gary Teale, before claiming his third with a neat finish from six yards three minutes from time.
The Seagulls, who knocked out Premier League big-spenders Manchester City in the last round, made a promising start and twice came close to opening the scoring inside the first six minutes.
First Thornton was denied by Rams goalkeeper Roy Carroll from 12 yards and moments later only a goalline clearance from Leacock prevented Stuart Fleetwood from scoring.
Albion had the ball in the net in the eighth minute. Fleetwood sprung the offside trap and set up Glenn Murray, who tapped home only to be denied by the linesman's flag for offside.
Derby finally came to life in the 12th minute but after the ball fell to Kazmierczak, he could not keep his effort down from 12 yards.
Five minutes later, team-mate Kris Commons also failed to hit the target from similar range following Kazmierczak's corner and then Ellington should have done better than head Commons' corner into the arms of Sullivan.
The visitors seemed to have taken control of the tie with two goals inside six minutes only to be pegged back by a Brighton side, who had been unbeaten in their last six games at the Withdean Stadium, when Elphick headed home.
Elphick nearly hauled Albion level in the 65th minute with another close-range header but Carroll kept the ball out before Villa claimed his second of the night to ease the Rams' nerves.
Villa had the chance to claim the match ball moments later but headed wide from six yards but was not to be denied a second time.
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