Fallon opened the Swindon scoring after on 3 minutes with a close range header after Andy Gurney had hit the bar.
On 21 minutes Fallon doubled Swindon's lead with another header which looked to be going wide, but just crept in.
Sam Parkin should have scored as well in the first half with only the keeper to beat, but the Luton 'keeper managed to save it.
Matt Hewlett put Swindon 3-0 up going into the break with a goal from close range on 44 minutes.
Luton rarely managed a goal on target through out the game, only managing a number of shot that either went wide or over, although in the second half Luton were unlucky not to have scored at least one goal.
In the second half Rory Fallon came closest to scoring a 4th for Swindon with a shot which beat the 'keeper but hit the post where the Luton 'keeper was able to save the rebound.
Andy King took Sam Parkin off to replace him with Tommy Mooney who came close but couldn't find the back of the net.
Overall a good important win for Swindon which moves them back up to 4th in the table, six points inside the play off's with only four games to go. Swindon's next game in the local away trip to Wycombe next Saturday.