Swindon started well with a couple of early corners, and McPhee did manage to get a shot, but it went over the bar.
On 23 minutes Steve Jenkins had to clear the ball off the line with a last second header after Liam Fontaine had beaten Rhys Evans.
Swindon were awarded a free kick just outside the box, but the ball taken by Aaron Brown struck the wall and went out for a corner. Swindon nearly took the lead from the corner, but the ball was just about tipped over the bar and away for another corner.
Then at the start of the second half on 49 minutes Aaron Brown gave Swindon the lead with a shot from the edge of the box which just crept in to give Swindon a deserved lead and give them a chance of staying up.
Steve Jenkins went off injured and was replaced by Andy Gurney after 62 minutes.
Then on 69 minutes Bristol City equalized with a shot from the edge of the box from Dave Cotterill which bat Evans and flew into the top corner of the net to make it 1-1.
Swindon wasted a number of chances to take the lead with Aaron Brown, Jamie Cureton, Lucas Jutkiewicz and Jack Smith all coming close to scoring.
Swindon also had a late penalty appeal for hand ball turned down as 5 minutes of stoppage time were played, but the ran of of time to take the lead.
At the game of the game their was a small pitch invasion by some Bristol City fans which did see one City fans being rugby tackled to the ground and lead away by Stewards which got a cheer from the Swindon fans.
Overall a good game, which Swindon had plenty of chances to win. A draw isn't any good for either side as it confirms Swindon's place in League Two next season, and ended any chance of Bristol City making the play off's, even though two months ago Bristol City looked like their would be relegated.