Swindon took an 18thminute lead through Billy Paynter who nodded home an excellent cross from Anthony McNamee.
The high-flying Dons had largely controlled the early stages of the game until McNamee produced his superb cross.
Despite the Dons' possession it was Swindon who might have increased their lead in the 24th minute when Simon Cox's low cross reached Paynter just three yards out but he failed to make contact.
The visitors were not to be denied however as a long throw by Jude Stirling was only half-cleared, and when Jemal Johnson knocked the ball back, Aaron Wilbraham fired his shot past Petr Brezovan for the equaliser.
Swindon should have regained the lead in the 35th minute when Kevin Amankwaah fed Hal Robson-Kanu on the right.
The winger produced an excellent low cross for Cox to run on to but, with the goal at his mercy, the striker saw his shot rebound off the bar and former Swindon star Sean O'Hanlon completed a timely clearance.
Swindon came out in a determined mood for the second half and once again Paynter was involved in the action. This time he broke on the right, carried the ball and his low drive beat the goalkeeper but came back off the post.
Cox's follow-up was parried by Willy Gueret before another Cox effort was blocked.
The Dons came back to claim a penalty when Luke Chadwick's shot appeared to be handled but referee Andy D'Urso waved away heated claims by the visitors.
From then on it was nearly all Swindon who created several excellent chances but it was just not their day in the penalty box.