Swindon had a couple of early chances but didn't take them. Barnet took the lead against the run of play after 18 minutes when Nick Bailey found the ball after it had rebounded out and scored fom 12 yards out.
Christian Roberts had the ball in the back of the net but his goal was ruled out for offside.
Swindon had a last minute corner at the end of the first half, but couldn't score and went into the half time break 1-0 down.
At half time Paul Evans came on to replace Michael Pook, and it was Evans who set up Ricky Shakes for Swindon's equaliser on 54 minutes when from the edge of the box Shakes scored with a shot which was more like a cross.
New goal keeper Peter Brezovan had a quiet night in goal after all the saves he had to make against Hartlepool, as Barnet didn't really have many more chances of scoring.
Royce Brownlie came on for Swindon on 79 minutes replacing Ricky Shakes, and so did Fola Onibuje who replaced Lee Peacock.
One minute into the three minutes of injury time Swindon scored to put them 2-1 in front with a 30 yard shot from Royce Brownlie.
Overall a fairly average game, but although they left it late Swindon did deserve to win, and now carry their 100% record into Saturday's home game against Rochdale.