John Obika scored in the last minute for a second successive season at the Keepmoat Stadium to deny Rob Jones his first win in caretaker charge of Rovers.
Doncaster showed great determination to battle back from a goal down and lead through a first senior goal for Keshi Anderson and a penalty from former Swindon striker Andy Williams.
But they were denied by Obika - who Rovers tried to sign in the summer of 2014 and scored the winner in the corresponding fixture last season – when he popped up with a last-gasp header.
Nicky Ajose had lobbed Town ahead moments after the re-start but just when the home side thought they had done enough to earn their first win in six attempts, Obika pounced from a poorly-defended corner.
Jones could take heart from the way his side dug deep after going behind but, with the club about to draw up their shortlist of possible replacements for Paul Dickov, could be made to rue the fact his side failed to hold on for his first victory in four attempts.
Jones had returned to the starting line-up, replacing the suspended Gary MacKenzie, but was forced off late in the first half.
He shuffled his pack, with debutant James Horsfield coming in at right back, and Harry Middleton and Richard Chaplow returning to midfield. Aaron Taylor-Sinclair, Paul Keegan and Cameron Stewart dropped to the bench.
There was a change to the shape too, with James Coppinger starting at the tip of a midfield diamond which had Richie Wellens at its base. With Swindon favouring a 3-6-1 formation, the change looked like a ploy to counter-act the Robins’ extra bodies in midfield.
Henrik Ojamaa enjoyed a lively start down Swindon’s right and, after the first bit of controlled passing from either side, only a timely block from Cedric Evina prevented him from testing Thorsten Stuckmann.
Wellens was doing his best to conduct things, acting almost like a quarter-back, but the only early opportunity for Rovers came when a ball dropped kindly for Anderson but he volleyed well over.
The clearest opening came when Chaplow slid in Anderson, a lively presence, but Swindon defender Jordan Williams did enough to put him off.
Some lovely wing play from Coppinger lit up an edgy contest and his cross from the left was on a plate for Williams who headed the best chance of the half wide.
After Jones hobbled off, Williams was presented with two chances to make amends just before half time. First he failed to control his effort following a drilled cross by Middleton and tenacious build-up play from Anderson, before seeing another shot deflected wide.
The second period started in disastrous fashion as a simple ball over the top from Ojamaa caught the Rovers rearguard flat-footed and Ajose casually lobbed Stuckmann.
Ajose should have doubled Swindon’s lead but, after being sent clear again, Stuckmann denied him.
In response Jones went for broke and replaced Middleton with Dany N’Guessan, who again made an impact from the bench. He sent a header straight at Tyrell Belford just after the hour – but it was not long before Rovers were level.
Anderson found space on the angle of the box and steered a delightful finish into the far corner.
The change in the atmosphere was palpable and N’Guessan almost fired Rovers ahead when he lashed a shot at Belford.
The game was turned on its head when Coppinger was tripped in the box and Williams coolly slotted home the resultant spot kick – before Obika had the final say.
Rovers: Stuckmann, Horsfield, Butler, Jones (Taylor-Sinclair 36), Evina, Coppinger, Middleton (N’Guessan 56), Wellens, Chaplow, Williams, Anderson (Forrester 87). Subs not used: Marosi, Gobern, Keegan, Stewart.
Swindon: Belford, Branco, Williams, Turnbull, Brophy, Traore (Hylton 83), Kasim, Thompson L, Ajose, Robert (Obika 72), Ojamaa. Subs not used: Johns, Ormonde-Ottewill, Balmy, Barry, Rodgers.