It was Huddersfield, who are 2nd in League One having not lost a single game all season who took the lead first on 22 minutes with a shot from Novak from just inside the area.
On 36 minutes Flint headed in a goal from close range from a Richie free kick to equalise.
Then 3 minutes later De Vita gave Swindon the lead with a goal from 10 yards out.
Huddersfield looked as if they would equalise in the second half, however it was Swindon who scored next. On 76 minutes Kerrouche scored from close range.
Then on 87 minutes Simon Ferry made it 4-1 to book Swindon's place in the second round.