Brezovan had to make a number of good saves to keep the score down, but it was 2-0 just before half time with a goal Jack Robinson from the edge of the area finding the top corner of the net making it 2-0.
Swindon had never looked like scoring and barely had an attack on goal all game.
By 73 minutes Dean Hammond made it 3-0 with his shot from the edge of teh area also finding the top corner of the net.
Aljofree was injured for much of the second half, but couldn't go off as Swindon had already made 3 subs with Comminges replacing Smith, Payner replacing Sturrock and McGovern replacing Mohamed in the first half.
Overall a very poor game with many Swindon fans leaving after the third goal. Swindon never looked like scoring, so it was an easy win for Brighton who weren't that good, but took their chances. The defeat leaves Swindon slipping down to 16th in the table ahead of next Saturday's home game against Hartlepool.