Swindon should have scored in the first half, and did get the ball in the back of the net, but Aljofree's header was ruled out after a foul in the box seconds earlier.
Aljofree should have scored a second first half goal but his shot which beat the 'keeeper was cleared off the line by the Luton defence.
Swindon took the lead after 56 minutes with a close range header by Lee Peacock finding the back of the net.
Ten minutes later Luton scored with a goal from Dave Edwards making it 1-1.
Luton cleared another Swindon shot off the line, and Swindon also had a penalty appeal turned down.
Then on 87 minutes Swindon were back in front after a close range goal from 7 yards out by Craig Easton, which was his first ever Swindon goal making it 2-1.
Overall a good win for Swindon who should have scored more goals. The win moves Swindon up to 4th place after just 2 games ahead of next Saturday's local derby away at Cheltenham Town.