Both sides went into the game with the score level at 1-1 from the 1st leg 4 weeks ago.
Alan Connell opened the scoring for Swindon on 17 minutes with a close range header leaving Barnet's 'keeper standing still to give Swindon a 1-0 lead.
Swindon continued to pile on the presure for the rest of the half, but couldn't get a second.
Barnet came out looking better in the second half, but couldn't score which was enough to give Swindon to win, and their second trip to the new Wembley in under 2 years.
The end of the game saw some of the 10,000 Swindon fans who braved to cold to watch come onto the pitch to celebate the fact that this is the first time they have ever reached the final of the Johnstones Paint Trophy.