Grant McCann's side were 2-0 up at the break and seemingly cruising but the Robins scored twice inside a minute just after the restart to salvage a point.
McCann made five changes with the entire defence from the midweek defeat to Bromley, along with Harry Clifton, all sitting this one out. And the freshened-up side wasted no time here, taking the lead with barely 20 seconds on the stopwatch. Swindon passed up possession from kick-off with George Broadbent clipping a though ball that Rob Street gleefully chased onto. He latched onto it, strode into the penalty area and coolly converted for his seventh goal in a Rovers shirt.
It got better midway through the half when Luke Molyneux made inroads down the right flank and picked out the unmarked Joe Sbarra who was in space and was allowed to caress a shot past the helpless Connor Ripley.
Swindon were restricted to half-chances in the opening 45 minutes but a triple sub at the break injected plenty of life into them and two of them got on the scoresheet in the space of a minute to remarkably pull the scores back to 2-2.
First, Daniel Butterworth lashed home a superb effort from outside the box that gave Ted Sharman-Lowe no chance. Then, fellow change Joe Westley got in front of his man at the near-post to prod home a leveller and stun the home fans.
Both sides toiled and Rovers had the best chances to win it, including a tap-in from sub Billy Sharp being chalked out for offside late on. But they were made to settle for only a point. They stay third, but their lead over fourth spot is now trimmed to just two points.
Here's our player ratings:
1. Ted Sharman-Lowe 6
Important double intervention in the first half, at 2-0, when he parried away a wicked Cotterill shot and then punched away a dangerous centre. No chance with Swindon's first goal but could maybe have done more for their second. Photo: Andrew Roe/AHPIX LTD
2. Tom Nixon 7
First league start for 14 months and in that respect he was more than comfortable with a solid defensive showing. Got forward when it allowed, too. Photo: Howard Roe/ahpix.com
3. Tom Anderson 6
Won his fair share of aerial duels but as the senior man in the backline he'll have been expected to do more to organise them in avoiding the second Swindon goal. Photo: Howard Roe/ahpix.com
4. Owen Bailey 7
Operated as a makeshift centre-half and was hardly flustered first half but had a tougher time of it in the second half. Fair share of interceptions. Photo: Bruce Rollinson/AHPIX LTD