It left Tranmere without a win in nine league outings and struggling at the foot of the table.
They were precious few chances in the opening period. It was marginally better later and Colchester missed two terrific chances to snatch the extra points late on.
Tranmere lacked inspiration despite the efforts of Stephen Jennings in midfield.
Subsitute Steve Davies was introduced for the last half hour and he made a big impact but Colchester were resolute and determined.
Skipper Kevin Watson set a superb example for United and there was also some excellent work from Wayne Brown.
Tranmere had the best first-half chance but an angled drive from Sam Aiston was turned over by keeper Aidan Davison.
Delroy Facey headed wide for Tranmere soon after half time and was off target with another effort in the 70th minute.
Then Davis headed over at the far post when set up by Facey.
Chris Iwelumo was unlucky with a 68th minute effort for Colchester and then fired over from close range when set up by Mark Yeates soon after.
The striker was also off target with another header in the 83rd minute.
Loan signing Jamie Cureton joined the action in the 79th minute and made an immediate impact.
But he wasted a super chance when firing wide from an unmarked position in the 84th minute and then two minutes later saw a close-range shot turned over the bar by alert keeper John Achterberg.