It was Tranmere who scored first on 34 minutes when Paul Hall scored with a 20 yard shot beating the diving Evans in the Swindon goal.
Swindon barely had a chance of scoring at all during the first half, with Tranmere having most of the play, including coming close with a free kick from the edge of the box.
In the second half Swindon looked better, but it was still Tranmere who looked the better side.
Swindon's first real chance to score came on 67 minutes when a poor Tranmere back pass found Christian Roberts who in a one on one with the 'keeper should have scored, but he took too long with his shot, and the 'keeper had time to make a good save.
However two minutes later Swindon did equalised when a cross found David Duke who scored from a tight angle from 10 yards out.
Swindon then very nearly took the lead when Steve Jenkins beat the 'keeper, but hit the post with a powerful shot from 30 yards.
Tranmere were soon back in the lead when Paul Hall scored a second from close range on 74 minutes.
Overall Tranmere did deserve to win as they were the better side. Swindon didn't play that badly, but they were restricted by Tranmere with Sam Parkin not been given any chance to score.
Swindon now take a two week break from the league, and play Sheffield Wednesday again next week in the first round of the FA Cup at the County Ground. Two weeks ago Swindon beat Sheffield 3-2 after coming from being 2-0 down with only 12 minutes to go.