Swindon played their part in a lively encounter but enjoyed little fortune in front of goal for the most part.
The visitors in fact made the better start but could not test keeper Danny Coyne with Simon Cox just failing to connect with a dangerous cross from Jon-Paul McGovern.
Tranmere went ahead from their first chance on 12 minutes. Steve Jennings and Miguel Comingees both challenged for a ball into the box by Shane Sherriff and it was Jennings who reacted best to leave keeper Petr Brezovan with no chance.
Sherriff brought a good save from Brezoven following a Paul McLaren free-kick before Swindon were unlucky not to equalise on 17 minutes when an excellent angled goalbound effort by Anthony McNamee was headed out from under the bar by Ben Chorley.
Chris Greenacre fired across the face of the goal and Jennison Myrie-Williams shot straight at Brezoven as Tranmere looked to double their advantage but Swindon, no win in their previous four outings, remained well in contention.
But there was disaster for the visitors on 40 minutes when Greenacre struck for Rovers from a deep corner by McLaren. Brezovan hooked the ball clear but the assistant referee signalled it had crossed the line. It took Greenacre into double figures for the season.
The Robins knew it was probably not going to be their night when a Hasney Aljofree effort soon after half-time was headed off the line by Robbie Stockdale.
But they kept going well and Billy Paynter gave them hope when netting from close range after a good run by Cox after 68 minutes.
Ian Moore brought the best out of Brezovan with a well-struck 79th-minute shot as Tranmere looked for a decisive third goal.