On the half hour mark Brentford got back into the game when May's shot from 12 yards beat Evans in the Swindon goal.
Unlike other games in the past few weeks Swindon didn't play well, and had few shots on goal, Brentford looked at times like they might be able to get a winner, or at least force a draw as the minutes ticked by and Swindon failed to get a second goal.
On 75 minutes Andy King bought on striker Rory Fallon replacing Andy Nicholas, this left Swindon with three strikers on the pitch with Parkin and Mooney also still up front. Fallon came very cose to getting a goal with his first touch the ball with a powerful header that the Brentford 'keeper just managed to save.
Swindon finally scored the winning goal on 82 minutes when Sammy Igoe hit the ball into the back of the net from 12 yards out. He then ran up to the bench and jumped on Andy King, followed seconds later by most of the Swindon team.
Swindon held on for the win, which makes it 5 wins in a row, and 11 games unbeaten. This is Swindon's longest winning run since March 1987 when Swindon won 7 games in a row.
Swindon travel to top of the table Plymouth next Saturday hoping to get closer to a top 2 finish.