Rovers picked up a single point from their home game against Kidderminster Harriers on Bank Holiday Monday.
Liam Hogan and Andy Mangan had given Rovers a two-goal lead but two late strikes by Gurjit Singh and Reece Styche gave Harriers a share of the spoils.
Tranmere made three changes to the side which started at Altrincham at the weekend with Andy Mangan, Nathan Blissett and Liam Hogan coming into the team.
Matt Hill returned to take a place on the substitutes bench.
Rovers dominated the early proceedings and Andy Mangan tested Kidderminster goalkeeper Alex Palmer from 25 yards in the opening ten minutes.
Adam Mekki had a deflected shot which went narrowly over the crossbar on 19 minutes and from the resulting corner, Tranmere took the lead. Liam Ridehalgh played a low cross from the left and Liam Hogan burst in at the near post to steer the ball home for his first Tranmere goal.
Harriers first shot on Scott Davies' goal came following a free-kick on the edge of the area on 24 minutes when the ball found its way to Joe Clarke whose shot went narrowly wide.
Rovers doubled their lead seconds later as a ball forward found Andy Mangan who burst clear, turned his marker inside and out before curling the ball past Palmer.
There was an opportunity to make it three on the half-hour mark when Ridehalgh's right-wing corner found Martin Riley at the back post but his effort was cleared away by the Harriers defence.
Harriers tested Davies on 42 minutes but a low shot from distance by Tahvon Campbell was dealt with by the Tranmere goalkeeper as the home side went in 2-0 to the good at the break.
Marlon Jackson was introduced into the action at the start of the second half in place of Adam Mekki.
His first action was on 47 minutes when he collected the ball 20 yards from goal and drilled a low shot narrowly across the face of goal.
A corner on 50 minutes from the right by Ridehalgh saw another effort on the Harriers goal as Maynard met the corner but could only head wide.
After Reece Styche tested Davies at one end, Maynard had another headed chance at the other as he met Jackson's deep cross only for Palmer to tip the ball over the bar.
Harriers began to exert some pressure on the Tranmere goal and Aman Verma had an effort turned over by Hogan before his deflected shot went just over the crossbar.
On 75 minutes, Jackson had a shot from 25 yards which was blocked into the path of Ridehalgh who was brought down. Mangan took the set-piece and forced a good save out of Palmer.
The visitors kept pressing and Verma had a header saved by Davies before Gary Brabin brought Michael Ihiekwe into the action in place of Nathan Blissett.
Kidderminster pulled a goal back on 84 minutes as substitute Gurjit Singh jinked past a couple of challenges before sliding the ball home off the post.
On 86 minutes, Mangan had a chance to score his second but his near post shot was well saved by Palmer.
Harriers levelled the game two minutes into stoppage time as the Rovers defence failed to clear a cross into the box and Styche knocked the ball past Davies.
Rovers managed to hit the post through Jackson before Ridehalgh fired wide in the final chance of the game.
Tranmere: Davies, Sutton Ridehalgh, Jennings, Hogan, Harris, Blissett (Ihiekwe 83), Maynard, Mangan, Riley, Mekki (Jackson 46). Substitutes: Turner, Hill, Margetts.
Kidderminster: Palmer, Hodgkiss, Maxwell, Clarke, Tunnicliffe, Styche, Wright (Verma 35), Campbell (Singh 66), Fox, Dawson, Rowe-Turner. Substitutes: Dinsley, Snedker, Green.
Referee: Stephen Ross
Yellow cards: Mekki (41), Styche (60), Riley (77)
Goals: Hogan (20), Mangan (25); Singh (84), Styche (90)
Attendance: 4622 (172 away)