It was a ding-dong battle on a raw night, but the Cumbrians took their chances well and defended stubbornly to deny the home side.
Carlisle had to play the last eight minutes with ten men after Paul Thirlwell was shown a red card for apparently taking a kick ant home sub Calvin Zola.
The visitors made a great start, with Danny Graham netting from close range in the tenth minute from a pass from Joe Garner.
It then needed a superb finger-tip save by keeper Kieren Westwood from a John Mullin shot to keep United ahead.
They then rode their luck as a Gareth Taylor shot was deflected for a corner off Westwood and a Mullin effort was kicked off the line by Garner.
Tranmere huffed and puffed to little avail in the second half. Chris Greenacre fired over with an angled shot and Steve Davies had no luck with two good efforts from just outside the area.
United almost snatched a second in the 52nd minute with a Garner shot shaving the outside of an upright.
But they did double their lead in the 67th minute when Kevin Gall netted from a cross by Graham after an error in the home defence.
Hartlepool's march towards League One continued with a comfortable win over Chester to extend their unbeaten run to 23 games and, overnight at least, their lead at the top of League Two to eight points.
They were in command for most of the game after taking an early lead, and coasted in after Chester had skipper Phil Bolland sent off for a second yellow card 20 minutes from the end. Andy Monkhouse and Ben Clark both scored in a 3-0 win for Pools.
David Healy capped the best week of his career with a last-minute winner to give Leeds United hope of staying in the Championship, and check his old club Preston's march towards promotion.
Brett Ormerod gave the Lilywhites an early lead at Elland Road, but Leeds roared back with an equaliser by Robbie Blake and Healy jubilantly struck his sixth goal in the space of seven days for club and country.
The win moved the Yorkshire side off the foot of the table, though they remain firmly rooted in the relegation zone with just six league games left to play this season.