Cheltenham lifted themselves off the foot of a very tight Division Two table with their first win since November 30th and only their sixth of the season.
The result was also a first victory for new manager Bobby Gould and a third game unbeaten for him since taking over at Whaddon Road.
Gould has already made his mark by introducing some innovative tactical changes to the side and he sprang another surprise by naming a very attacking line-up for this game.
The move nearly backfired when Stuart Barlow hit the post for Tranmere early on, but Cheltenham were celebrating an early goal themselves after eight minutes when loan signing Marvin Brown smashed in a 30-yard rocket for his first Football League strike.
Tranmere goalkeeper John Achterberg saved well from Julian Alsop and Martin Devaney blazed wide as Cheltenham continued to shade an entertaining game.
But they were pegged back five minutes after the break when Ian Sharps scored from close range after goalkeeper Steve Book had failed to make proper contact when punching clear a Mickey Mellon corner.
Undaunted, Cheltenham stuck to their task and scored for the second time when Martin Devaney, a tricky wide player and their most effective player on the night, crossed for veteran marksman Tony Naylor to score with a close- range header.
Devaney added the third himself in the 72nd minute when he accepted a return pass from Naylor and drilled a shot under substitute goalkeeper Russell Howarth, Achterberg having gone off with a leg injury.
This was the first time that Cheltenham had scored three goals in a league game this season and boss Gould said: "The confidence is there and the players have accepted the challenge before them.
"We have to take this on game by game and accumulate the points we need as there are still 51 to play for." Disappointed Tranmere boss Ray Mathias said: "Credit to Cheltenham for playing well but it will be a quiet coach home tonight because we know we can do much better."