Tranmere finished 2013 with a 3-1 away defeat at Sheffield United.
Goals from Jamie Murphy, Jose Baxter and Ryan Flynn earned the Blades the victory, with Ash Taylor pulling a goal back late in the game. The result leapfrogged Nigel Clough's side above Rovers who dropped to 20th in League 1.
Ronnie Moore made one change to the team that beat Shrewsbury as a head injury forced James Wallace to be replaced by Steve Jennings in midfield.
Owain Fon Williams easily saved Harry Maguire's header from a free kick in the sixth minute but two minutes later the home side took the lead. A corner from the right was headed goalwards and into the path of Jamie Murphy who controlled, turned and fired past Fon Williams from close range.
It was almost two three minutes later, but Ryan Flynn's 25 yard effort went just past the left hand post, while Stephen McGinn fired over from the edge of the area on 18 minutes.
Rovers had a chance to level on 19 minutes. Ryan Lowe ran on to a high ball down the left from Evan Horwood and headed the ball past Blades keeper George Long. The striker did well to keep the ball in play but had a tight angle to shoot from allowing Maguire to race back and clear his effort off the line.
At the other end Taylor sliced a clearance against the Tranmere bar, with the ball bouncing on the line and away from goal before being cleared by Liam Ridehalgh.
Danny Holmes shot wide from a Jason Koumas corner on 30 minutes and a minute later Lowe forced a good save out of Long after running on to a pass from Andy Robinson.
Taylor cleared a header from McGinn on 36 minutes and Fon Williams pushed a Ryan Flynn cross away from goal a minute later.
It needed a superb block from Holmes to keep McGinn's shot away from goal on 40 minutes but the defender picked up a knock in the process and was replaced by Max Power soon after.
Rovers could have been level a couple of minutes into the second half after Long miss hit a clearance and was out of his goal, but Robinson sent his left foot shot wide of the open goal from 35 yards.
However, on 56 minutes the Blades went 2-0 up, with Jose Baxter finding the net from 12 yards from a Chris Porter cross.
It needed a well timed challenge from Power to deny Murphy a shooting opportunity at the back post on 59 minutes while Fon Williams did well to palm Michael Doyle's shot away from goal moments later.
Jean-Louis Akpa Akpro and Jake Kirby replaced Chris Atkinson and Andy Robinson with half an hour remaining but soon after United added to their tally when a counter attack down the left from Murphy was converted by Flynn from 12 yards.
Fon Williams pulled off a fine one handed save to keep out Porter's curling shot from the edge of the area on 80 minutes while substitute Simon Lappin flashed a shot past the right hand post from 25 yards three minutes later.
Rovers pulled a goal back on 85 minutes. A foul on Akpa Akpro gave Koumas a free kick wide on the left and his cross found Taylor who controlled and fired into the bottom left corner from 12 yards.
There was almost a second on 90 minutes but Kirby's 30 yard volley went inches over the bar, the final shot of the game for either team.
Sheffield United: Long, Maguire, Hill, Flynn (Cuvelier 83), Doyle, Porter, Baxter (Coady 70), McGinn (Lappin 75), Collins, Murphy, McMahon. Substitutes: Howard, Taylor, Brandy, Kennedy.
Tranmere: Fon Williams, Holmes (Power 43), Taylor, Ridehalgh, Horwood, Peterson, Koumas, Jennings, Atkinson (Akpa Akpro 61), Robinson (Kirby 61), Lowe. Substitutes: Mooney, Rowe, Stockton.
Referee: David Webb
Yellow cards: McGinn (27), Robinson (51), Maguire (60), Akpa Akpro (64), Jennings (79)