Ryan Lowe's 14th goal of the season wasn't enough for Rovers as a goal in each half from Adebayo Akinfenwa gave Gillingham a 1-2 win at Prenton Park.
Akinfenwa's first came in first half injury time and the second after Jim McNulty's red card had left Rovers with ten men.
Lowe gave Rovers hope 15 minutes from time but they were unable to find the equaliser.
Ronnie Moore made three changes to the team that started at Carlisle, Three changes for Rovers as Danny Holmes, James Wallace and Jake Kirby came in for Jon Otsemobor, Max Power and Chris Atkinson.
Cody McDonald and Bradley Dack missed early shots for Gillingham while Owain Fon Williams pulled off a fine one handed save to keep out an effort from Myles Weston after he took advantage of a slip from Ash Taylor to get one on one with the keeper.
After a slow start Rovers started to improve. Ryan Lowe headed just past the left hand post on 13 minutes from Wallace's right wing cross and Jean-Louis Akpa Akpro chipped inches wide after running on to a quickly taken free kick.
Weston curled past Fon Williams but also past the left hand post from the right side of the Rovers area on 18 minutes, but the winger left the pitch soon after nursing an injury and was replaced by Antonio German.
After Wallace had been fouled five yards outside the Gillingham area Koumas curled a free kick over the bar while Kris Peterson couldn't head goalwards from Kirby's right wing cross after Lowe's shot had been blocked on 33 minutes.
Stuart Nelson had to dive to his left to palm Wallace's bottom corner-bound effort past the post on 42 minutes and the keeper easily claimed Ash Taylor's header from the resulting corner.
With the sides looking set to be level at half time, Gillingham took the lead in first half injury time. A shot from Dack was blocked and Taylor's clearance was deflected into the path of Adebayo Akinfenwa who fired a first time shot past Fon Williams and into the right side of the net.
The visitors had a chance to level early in the second half. McDonald flicked the ball past Ridehalgh and outpaced the defender before seeing his low shot saved by Fon Williams and Ridehalgh reacted quickly to block the follow up effort from Jake Hessenthaler. A minute later Dack hit the side netting from close range after running on to a pass from McDonald.
Rovers were reduced to ten men on 55 minutes. McDonald broke past McNulty, cut in towards the area and was tugged back by the defender who was shown a straight red card as the last defender.
Evan Horwood replaced Kirby and moments later Lowe had a chance to level following a mistake from Adam Barrett, but the striker missed the target from the edge of the area. Fon Williams pulled off another fantastic save to keep out Barrett's close range header from a corner on 59 minutes.
But the Gills doubled their lead ten minutes later. A cross from Steven Gregory reached Akinfenwa at the back post and after his first header hit the post, the ball rebounded straight to him and he nodded into the net from close range.
Cole Stockton and Andy Robinson replaced Akpa Akpro and Peterson and it was Robinson who provided the assist for Lowe's 14th goal of the season on 77 minutes. The midfielder's high ball down the middle was controlled by Lowe inside the area by Lowe, knocked past the onrushing Nelson and then past two defenders on the line into the net.
Stockton fired over the bar from 25 yards in injury time, while Nelson saved Wallace's low strike with virtually the last kick of the game.
Tranmere: Fon Williams, Holmes, Taylor, McNulty, Ridehalgh, Kirby (Horwood 57), Wallace, Koumas, Peterson (Robinson 72), Lowe, Akpa Akpro (Stockton 64). Unused substitutes: Mooney, Otsemobor, Power, Atkinson.
Gillingham: Nelson, Martin, Legge, Akinfenwa (Lee 72), McDonald, Weston (German 22), Gregory, Dack, Harriman, Barrett, Hessenthaler. Unused substitutes: Howard, Davies, German, Lee, Fagan, Daniels, Hare.
Referee: Rob Lewis
Yellow cards: Dack (34), Nelson (77), Robinson (81)
Red card: McNulty (55)