They will meet either Hartlepool or Bristol City at the Millennium Stadium if they can hang on to the lead given them by Carpenter in a dire match at the County Ground.
Carpenter snapped up the only goal with a shot after 72 minutes which struck Swindon defender Andy Nicholas to deceive goalkeeper Rhys Evans.
It was Brighton's only shot on target in the entire game but Swindon had no answer. Andy King's men had plenty of possession but hardly ever made it look like paying off.
Swindon twice struck the woodwork and Tommy Mooney should have done better with a free header in the first half from six yards. But overall Brighton's gameplan to frustrate and smother their opponents was a huge success.
Swindon's second biggest crowd of the season, in excess of 14,000, had to wait until the 34th minute before they saw a piece of meaningful action with Andy Gurney slicing wide before Sam Parkin crossed for Mooney to go full length, only to head wide when a goal looked certain.
Brighton's leading scorer Leon Knight was booked for a foul in the 42nd minute, but then on the stroke of half-time Sammy Igoe got in a right-foot shot from the edge of the area, slightly deflected by Carpenter but enough to strike an upright.
It was the same story in the second half with Brighton content to soak up plenty of pressure and Swindon unable to break them down.
But after 62 minutes they almost broke the deadlock, when substitute Grant Smith crossed from the left and Mooney, racing to the near post, saw his shot from six yards hit the underside of the bar.
The rebound fell awkwardly for Parkin, but his goalbound header was tipped over in spectacular fashion by Ben Roberts.