An own goal from Ash Taylor gave Sheffield United all three points at Prenton Park on Good Friday.
It was an otherwise close game with neither keeper really tested until late in the match and Rovers going closest through substitute Adam McGurk.
There was one change to the team that defeated Stevenage with new loan signing Sean McGinty replacing Paul Black at left back. McGurk was named among the substitutes after recovering from injury.
Rovers started brightly and won three corners on the left hand side in the opening five minutes, though each set piece was met by a Sheffield United head.
A 30 yard shot from Ash Taylor deflected wide for a corner on 13 minutes from which Ben Gibson headed wide from Power's cross.
Jonathan Forte fired across goal and wide for the visitors on 14 minutes and the striker saw another effort deflect past the post six minutes later.
It needed a strong hand from Owain Fon Williams to keep out Forte's next attempt on 24 minutes, with the former Scunthorpe United player firing towards the bottom left corner under pressure from McGinty and Ben Gibson.
Fon Williams saved again from Forte on 34 minutes and two minutes later a flick header from Dave Kitson went wide of the target.
The visitors took the lead on 41 minutes. A free kick from Tony McMahon was played into the Rovers area and Taylor's attempt at clearing the ball was sliced past his own keeper into the bottom right corner of the goal.
An overhead kick from McGinty from an Abdulai Bell-Baggie cross landed on the roof of the net two minutes into the second half and a 25 yard effort from Max Power deflected wide of the target.
McGurk replaced Bell-Baggie on 65 minutes and soon after Akpa Akpro volleyed wide of the target from a Sidibe flick on.
Barry Robson brought a save out of Fon Williams with a left foot drive from outside the area on 73 minutes while a McGurk effort deflected straight to George Long nine minutes later.
A long range Ryan Flynn strike crashed against the Tranmere bar on 84 minutes before being cleared by Danny Holmes and Gibson and Fon Williams had to tip a shot from Robson from a similar distance over his goal soon after.
Tranmere: Fon Williams, Holmes, Taylor, Gibson, McGinty, Bell-Baggie (McGurk 65), Power, Palmer, Bakayogo, Sidibe, Akpa Akpro. Substitutes: Mooney, Kay, Goodison, Harrison, Stockton, O'Halloran.
Sheffield United: Long, Maguire, Hill, Flynn, Doyle, MacDonald, Kitson, Collins, Forte (Poleon 90), Robson, McMahon. Substitutes: Westlake, Higginbotham, Porter, Ironside, McFadzean, Coyne.
Referee: Andy Haines
Yellow cards: Flynn (38), Maguire (40), Sidibe (77)