Bristol Rovers took the lead on 12 minutes when a free kick from Bristol Rovers 'keeper Steve Phillips found Richard Walker who scored with little problems.
But on 15 minutes Swindon were level with Lucas Jutkiewicz shot from the edge of the area took a deflection and ended up in the back of the net.
Then on 17 minutes Swindon took the lead with Weston's 30 yard shot hitting the bar, and bouncing down and back out, so Aaron Brown headed the ball into the bacl of the net, but it was too late as the goal had already been given for Weston's shot.
Both sides had more chances to score, but Swindon went into the half time break still winning 2-1.
Christian Roberts picked up his 5th yellow card of the season meaning he will now be suspended for next Saturday's away trip to Macclesfield.
Bristol Rovers came close a few times to getting an equaliser, but Phil Smith made some good saves, and they hit the ball wide a few times, and Swindon held on until the end.
Overall a good game, which Swindon did deserve to win. There was a small amount of crowd trouble inside the ground towards the end of the game with seats being thrown between both set of fans in the Arkells Stand. Swindon now travel to Paul Ince's bottom of the table side Macclesfield next Saturday.