A goal in each half gave Shrewsbury Town a 2-0 win at Prenton Park on Friday night.
Liam Palmer's early red card followed by a goal for the visitors gave Ronnie Moore's side a difficult task for the remainder of the game.
Rovers pushed for an equaliser in the second half but the Shrews' second goal midway through the half effectively ended the contest.
Ronnie Moore made one change to the starting XI that began the game at Leyton Orient seven days earlier with Michael O'Halloran replacing David Amoo. New loan signing Paul Corry was named among the substitutes in place of Michael Kay.
After a team huddle before kick off, Rovers started brightly. Donervorn Daniels sent a header into the arms of Chris Weale from Zoumana Bakayogo's deep free kick and Adam McGurk curled wide following a surging run through the Shrewsbury half from Max Power.
At the other end Liam Palmer got an important block in as the Shrews pressed from a free kick.
However, Rovers' hopes to an early hit on six minutes when Palmer was shown a straight red card for a challenge on Joe Jacobson inside the Shrewsbury half.
And four minutes later the home side found themselves a goal down. Owain Fon Williams uncharacteristically dropped a cross from the left wing in the middle of his penalty area and Shrewsbury debutant Chris Porter stroked into an empty net.
Rovers tried to work their way back into the game but stray passes didn't help their cause, though McGurk did fashion a shooting opportunity on 14 minutes, with his effort going past the far post.
Paul Parry fired high and wide from 25 yards for the visitors on 21 minutes while Cole Stockton flashed a header just past the far post four minutes later from McGurk's cross.
Fon Williams did well to palm David McAllister's low shot from 20 yards past his right hand post on 35 minutes while McGurk's long range effort at the other end brought a save out of Weale in first half injury time.
Daniels headed a Robinson corner wide of goal in the second minute of the second half and Fon Williams saved a 20 yard attempt from McAllister.
A 30 yard right foot effort from Robinson was comfortably saved by Weale in front of his bottom left hand corner and Stockton's volley from inside the Shrewsbury area went over the target as Rovers pressed for an equaliser.
The visitors should have been two up on 58 minutes. Breaking on the counter attack with an extra man, they first saw Porter miss his attempt at a shot before Steve McGinn blazed over from 12 yards.
O'Halloran turned his marker on the halfway line on 60 minutes and raced towards the Shrewsbury area only for his 20 yard shot to be blocked, while a cross spilled by Weale was cleared by his defence before Rovers could capitalise.
Ash Taylor cleared off the line on 63 minutes but soon after the Shrews doubled their lead. After Fon Williams had pulled off a fantastic reaction save to keep out Porter's close range header, Cameron Gayle headed in from the resulting corner after Fon Williams collided with Holmes inside the six yard box. The defender had to be replaced by Danny Harrison before play could restart.
Daniels' long range effort failed to trouble Weale on 78 minutes and Robinson shot wide from outside the area three minutes later.
Tranmere: Fon Williams, Holmes (Harrison 70), Taylor, Daniels, Bakayogo, McGurk, Power, Palmer, Robinson, Stockton (Corry 68), O'Halloran (Amoo 81). Substitutes: Mooney, Goodison, Black, Bell-Baggie.
Shrewsbury: Weale, Jacobson, Jones, Richards, Morgan (Rodgers 78), Parry (Purdie 85), McAllister, McGinn, Edwards, Gayle, Porter. Substitutes: Anyon, Mambo, Summerfield, Bradshaw, Wildig.
Referee: Mark Brown
Yellow cards: Taylor (52)
Red cards: Palmer (6)