Unlike Andy King would have done Iffy Onoura played a full first team with Christian Roberts also starting behind Fallon and Bouazza up front.
Swindon took the lead after only 4 minutes with a header from Rory Fallon after a cross from McDermott.
Christian Roberts also came close with a shot from 20 yards out which was well saved by the Stevenage 'keeper and pushed out for a corner. Roberts had a good game, and also should have scored with a shot from 5 yards out, but he hit the ball with so much power that it flew past the goal and finished up near the corner flag.
Swindon had most of the ball in the first half with Stevenage just being reduced to a full long distance shots, and a couple of corners which were cleared away without any problems. Tom Heaton had a quiet night in the Swindon goal keeping his second clean sheet in a row.
Michael Pook also came close to scoring with a powerful shot from 25 yards out which beat the 'keeper but hit the bar. It struck with stuck force that the ball rebounded out and over the roof of the empty Town End stand.
In the second half Swindon had fewer chances to score than in the first, but doubled their lead after 53 minutes following a free kick where Fallon just missed the goal only for loan signing Bouazza for score from an acute angle to make it 2-0 to the home side.
The game was watched by a poor crowd of only 1,771 with only one stand - the Arkells stand being opened, but most of the crowd went away happy after Iffy Onoura's first win as manager.
The game finished 2-0 which was a fair result overall, although a few more goals would have better reflected all the chances Swindon had. The draw for the second round of the LDV Vans Trophy takes place on Saturday morning before the home league game against Scunthorpe.