Bristol City nearly took the lead after 13 minutes when a mistake from Steve Book who cleared the ball straight to a Bristol City player, but Book then managed to force Leroy Lita's shot away for a corner.
Both sides had limited chances in front of goal, with Bristol City trying to beat Book with a 40 yard lob, which he mananged to catch, although it would have gone wide anyway.
The start of the second half was much the same as the first half with neither side getting much of a chance in front of goal.
The only goal of the game came on 64 minutes when Sam Parkin scored from close range after an Andy Nicholas cross.
Bristol City pushed for an equaliser with Steve Book being forced to make a couple more good saves. On 76 minutes a free kick from Bristol City's Bell hit the bar, but was cleared away to safety.
Despite some last minute pressure Swindon held on to beat Bristol City for a second time this season, and book themselves a place in the LDV Vans Southern semi final.
Overall it was a fair result, as Swindon looked the better side, but they didn't get many chances in front of goal. Swindon's are at home again this Saturday in the FA Cup second round against Notts County.