Luton took the lead on 31 minutes when ex Bristol City striker Tony Thrope put them into the lead with a header.
Stefani Miglioranzi put Swindon back in the game just before half time with a curling shot from 25 yards.
A minute later Swindon were back in the lead with Sam Parkin getting his 26th goal of the season with a close range shot.
In the second half Matt Heywood should have made it 3-1 when the ball fell to him about 10 yards from goal where he just had to tap the ball in, but inside he kicked it with all his power and the shot hit the bar, it looked like it might have then crossed the line, but the goal wasn't given. Luckly this didn't matter as Swindon went on to keep their 2-1 lead.
Swindon now finish the season in 10th, with 60 points their highest finish for a few seasons. Last season they managed to finish 13th. Maybe next season Swindon will be able to reach the play off's as long as Sam Parkin stays at the club, and scores as many goals as this season.