Isaac Olaofe scored the only goal of the match in the 70th minute as the Yellow Army climbed into the top eight while Tranmere are now winless in their last four league matches.
Sutton won their third straight 1-0 match in all competitions while picking up their first league win since October 26th and second consecutive away from home.
Story of the match
Tranmere had a succession of corners that resulted in a good opportunity in the 24th minute when Callum McManaman curled one from the edge of the area that trickled just wide.
It was the visitors turn to threaten just before halftime as David Ajiboye sent a teasing ball into the box for Will Randall and his looping header at the back post was only kept out by the woodwork.
Moments later, Ajiboye had a go after getting by McManaman, but after being slightly off-balance, sliced his shot wide.
At the other end, the hosts broke on a swift counter-attack that resulted in a left-footed strike by Liam Feeney that sailed wide of the near post.
The Yellow Army kept up the pressure in the second half, Randall shooting just high, Ben Goodliffe heading back Rob Milsom's free kick back from the right and Coby Rowe volley beat Ross Doohan, but was cleared off the line by Peter Clarke.
The home captain denied U's again soon afterwards as Richie Bennett battled through on the left and Clarke dived in to divert his shot wide for a corner.
On the hour mark, Tranmere manufactured their first chance of the half. Josh Dacres-Cagley delivered a cross from out wide that Eliott Nevitt rose highest for, but couldn’t guide his header on target.
Sutton finally broke the deadlock when Olaofe stole possession from Clarke, who was trying to play out from the back, glided forward and slotted home one-on-one against Doohan.
Tranmere had half-chances late on, Dean Bouzanis making an awkward save at the second attempt from a McManaman volley and Ryan Watson went close with an effort from the edge of the box.
Man of the match: Isaac Olaofe
You could argue that the spell of pressure was started when Ajiboye set up a couple of chances late in the first half and that carried over, but Olaofe gets the nod because he started the match-winning sequence by stealing the ball, raced downfield and finishing things off with a goal.