Alex Revell gave Swindon the lead after only 8 minutes with a close range goal after a McGovern cross.
On 21 minutes Ben Hutchinson made it 2-0 with an excellent shot finding the back of the net.
By the time the second half started Brentford were looking at lot better, and their were unlucky several times which including them hitting the bar, and missing an open goal with the rebound.
Finally after much pressure Brentford pulled a goal back on 78 minutes to make it 2-1 with Carl Cort.
A minute later Swindon had extended their lead again with a powerful shot from Alex Revell.
Then 3 minutes later Brentford scored again with Charlie McDonald scoring from close range after a corner to make it 2-3.
Swindon held on for the final 10 minutes to end their run of draws, and move them back up into the play off's. Overall an excellent game which Swindon derserved to win. Swindon now return to Devon on Tuesday night to play Exeter again, this time in the Johnstone's Paint Trophy.