Rovers were narrowly beaten 1-0 at home against top of the table Cheltenham Town.
An early Danny Wright goal was the decisive strike to help the Robins extend their unbeaten league run to 21 matches.
Manager Gary Brabin made just one change to the side which drew 0-0 with Aldershot Town last week, with Gary Taylor-Fletcher replacing Jack Mackreth who took a place on the bench.
It was a frantic start with Lee Vaughan clearing off the line just 90 seconds in while James Norwood almost found Michael Higdon inside the penalty area moments later.
On three minutes, Cheltenham took the lead as Danny Wright got the better of his marker and fired home past Scott Davies from 15 yards.
It was end to end with Davies the busier goalkeeper, palming away a dangerous low cross by James Rowe, with the same player testing the Rovers goalkeeper again with a shot from 20 yards.
Rovers came into the game more as the half went on and Gary Taylor-Fletcher fired narrowly wide while Higdon had a header well saved by Dillon Phllips in the Cheltenham goal.
The first half whistle blew as Davies made a magnificent save from James Dayton.
The second period began with The Robins having a couple of good chances as first James Dayton and then Wright missed the target from the edge of the box.
On 59 minutes, Adam Mekki was introduced into the action in place of Gary Taylor-Fletcher.
Midway through the second half, Dan Holman tried to lob Davies from 25 yards but the Rovers shot-stopper got back and acrobatically tipped the ball out of play for a corner.
On 70 minutes, Jake Kirby was brought into the fray as he replaced Jeff Hughes.
The substitute's first action was to shoot from 12 yards which Phillips saved.
With 10 minutes remaining, Norwood did well on the right and fed the ball back to Mekki whose cross fizzed across the face of goal and wide.
On 88 minutes, Mekki's corner was met by the head of Lois Maynard but his effort was straight at Phillips who made the save.
Cheltenham held on despite more late pressure and broke a club record of 21 matches unbeaten in the league.
Tranmere: Davies, Vaughan, Ihiekwe, McNulty, Ridehalgh, Taylor-Fletcher (Mekki 59), Harris, Maynard, Higdon, Norwood, Hughes (Kirby 70). Substitutes: Turner, Sutton, Mackreth.
Cheltenham: Phillips, Barthram (Munns 74), McLennan, Storer, Parslow, Wright, Hall, Burgess, Rowe, Dayton (Cranston 65), Holman. Substitutes: Kitscha, Waters, Lymn.
Referee: Martin Coy
Yellow cards: Dayton (23), Munns (90), Harris (90)
Goals: Wright (3)
Attendance: 5418 (318)