Play was never easy in the wild conditions but Tranmere got the vital breakthrough after an hour with a second goal of the season for Calvin Zola.
There were few goal chances in the opening period. Andy Taylor missed the target with two long range efforts for the Merseysiders and Shane Higgs in the Town goal dealt confidently with shots from Shane Sherriff, Zola and a Paul McLaren free kick.
Home keeper Danny Coyne held on comfortably to an early shot by Steve Gillespie for the visitors whilst Adam Connolly wasted a great chance on the half hour when firing wide after being set up by Paul Connor.
Cheltenham started the second half in lively form but could not capitalise on four corners.
McLaren shot wide from 25 yards for Tranmere and Higgs made a diving save at the feet of Chris Greenacre.
The vital breakthrough came on the hour with Zola netting his second goal of the season from eight yards after good build up play involving McLaren, Jennison Myrie-Williams and Greenacre.
Cheltenham rang the changes in the last half hour to try to salvage a point. Ben Gill fired over from 30 yards, an effort by Michael D'Agostino was deflected for a corner and Ashley Vincent headed wide.
Tranmere should have doubled their advantage in the 90th minute. Myrie-Wlliams made a great run through but then shot wide from just six yards.
In injury time home keeper Danny Coyne had to move sharply to tip aside a deflected shot by Vincent.
The result was possibly tough on Cheltenham who are now deep in relegation trouble after their ninth defeat away from home.