Rovers picked up a point from the Merseyrail Community Stadium after a 2-2 draw against Southport.
The home side went into a 2-0 lead in the first period through Gary Jones and Mike Phenix before a second half response from Jay Harris and James Norwood meant the points were shared.
Southport also had a player sent off in the second half as Luke Foster saw red for a challenge on Marlon Jackson but they held off the Tranmere pressure to claim a point.
Tranmere manager Gary Brabin named an unchanged side for the visit to his former club Southport. The only change from the squad which beat Chester FC 2-0 on Saturday came on the bench with Marcus Holness taking the place of Liam Ridehalgh.
After a quiet opening quarter of an hour, the home side took the lead as Andy Bishop laid the ball off to Gary Jones who struck a low, powerful shot past Scott Davies.
Southport doubled their lead on 20 minutes as Louis Almond and Bishop exchanged the ball to Mike Phenix who turned past his marker and shot home.
Rovers came a lick of paint away from getting a goal back on 36 minutes when Andy Mangan struck a free kick from 30 yards which bounced back out of the post before Southport cleared as they took a first half 2-0 lead in at the break.
Tranmere came out of the blocks quickly at the start of the second half and got a goal 30 seconds after the restart after James Norwood's shot was saved by Andy Coughlin with Jay Harris tapping home the rebound.
The equaliser came a minute after Rovers made a substitution with Marlon Jackson replacing Andy Mangan. Norwood received the ball on the left edge of the penalty area and slammed the ball past Coughlin to make it 2-2.
After further pressure on the Southport goal, the hosts were reduced to 10 men after 64 minutes when Luke Foster received a red card from referee Joe Johnson following a tackle on Jackson.
On 71 minutes, Matt Hill's cross took a wicked deflection off Liam Nolan which almost flew into the net but went just wide of the target.
Rovers pushed for a winning goal but the stubborn Southport defence stood strong and held on to share the spoils.
Southport: Coughlin, Challoner, Nolan, Foster, Wright, Bishop (Allen 57), Jones, Rutherford, Almond (Joyce 68), Davies, Phenix. Substitutes: Viscosi, McCarthy, Cameron.
Tranmere: Davies, Ihiekwe, Sutton, Hogan, Hill, Harris, Jennings, Dawson, Mekki, Mangan (Jackson 56), Norwood. Substitutes: Turner, Maynard, Holness, Blissett.
Referee: Joseph Johnson
Yellow cards: Phenix (51), Jennings (74)
Red cards: Foster (64)
Goals: Jones (15), Phenix (20); Harris (46) Norwood (57)