Tranmere led by two goals at the interval and there might have been more against a shaky Swindon defence which let in seven at Nottingham Forest little more than a week ago.
Chris Greenacre gave Tranmere the lead in the 21st minute after a pass from Calvin Zola had opened up the frail Swindon back four.
Greenacre swept home his 15th goal of the season with a left-foot shot from just inside the area.
Swindon had their chances with a header from Lee Peacock bringing a smart save from Dino Seremet in the 14th minute and Trevor Benjamin heading just wide.
Tranmere went further in front in the 33rd minute when Sam Aiston was allowed to run from inside his own half and exchange passes with Zola before bearing down on goal and seeing his deflected shot off goalkeeper Rhys Evans fall into the net.
Swindon were booed off the pitch at half-time by their disappointed fans but they got more for their money after the interval.
Sean O'Hanlon headed narrowly over the bar in the 51st minute and the introduction of Ricky Shakes as a substitute at the start of the second half revitalised the home team.
Swindon pulled a goal back in the 69th minute when Jamie Cureton got into the area and scored with a low right-foot shot for his fifth of the season.
Swindon staged a rousing finale but Benjamin headed narrowly wide from a good position as Tranmere held out.
Prominent for Tranmere in midfield was the veteran Jason McAteer who made several outstanding passes to keep Swindon penned in their own half during the first period.