Chris Shuker set up both second-half goals for Tranmere to put an end to a poor run of home results for Rovers.
Bas Savage headed home at the far post from a Shuker cross with the visitors temporarily down to 10 men as James Wesolowski received treatment.
In the final minutes Shuker made his presence felt again, first hitting the post in the 87th minute, before he then set up Edrissa Sonko to head in.
Earlier in the second half Shuker missed the target with a fine strike.
Tranmere: Coyne, Shotton, Chorley, Goodison, Taylor, Moore, Jennings, Kay, Edds (Sonko 66), Shuker, Savage.
Subs Not Used: Antwi, Greenacre, Ahmed, Achterberg.
Booked: Shotton, Jennings.
Goals: Savage 69, Sonko 89.
Cheltenham: Scott P Brown, Kenton, Rowe-Turner, Diallo, Wright, Lindegaard, Montrose, Wesolowski (Owusu 71), Ridley (Vincent 64), Connor, Fleetwood (Gallinagh 79).
Subs Not Used: Higgs, Armstrong.
Booked: Ridley.
Att: 4,535
Ref: Michael Oliver (Northumberland).
Cheltenham boss Martin Allen told BBC Radio Gloucestershire:
"We weren't spectacular, it looked to me like a professional display, it certainly wasn't breathtaking but up until they scored we weren't in any danger."
"As the game was going to evolve we were going to bring on some forwards to try and win us the game."
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