Charlie Austin opened the scoring for Swindon on 22 minutes with a goal from 8 yards out.
Hartelepool's closest chance of the game came during the first half when a powerful shot hit the bar, but didn't go in.
The second half was uneventful, although Hartlepool did come close to getting a late equaliser, but Swindon held on for the win.
This leaves Swindon in 4th place , just one point off second place Leeds who Swindon face on Saturday.