Colchester moved up to third place in the table courtesy of a strike from Wayne Andrews, but they might have had more and Wrexham claimed they should have earned at least a point.
A delighted Colchester boss Phil Parkinson said: "We were excellent, disciplined and good on the ball. I'm really proud of the lads they were magnificent.
"Now we have moved up to third, the difficult thing is to stay there and keep the run going." Wrexham manager Denis Smith complained that his players had faced three games in six days because of re-arranged fixtures, he said: "We didn't turn up for the first half. The second half we dominated, but their keeper was inspired.
"If we have as many chances as we had in that game, we should score at least once." Wrexham made a slow start, reduced to long pot-shots from Jim Whitley, Carlos Edwards and a Darren Ferguson free-kick that went straight into the hands of keeper Simon Brown.
Kem Izzet headed over for Colchester and Craig Fagan shot wide before Andrews ran on to a chip from Fagan, rounded the keeper and finished from six yards.
Andy Myers nearly added a second with an angled shot against the crossbar and Andrews missed a clear chance, shooting straight at the keeper.
Wrexham improved after the break while Colchester packed their defence and held their lead.
Brown turned a powerful drive from Edwards round the post at full stretch and saw a Ferguson shot deflected wide.
Wrexham gambled by putting on Chris Armstrong as a third striker in their desperate bid for a goal, following his long injury lay-off.
Edwards had another shot blocked on the line and Stephen Roberts was out of luck when his shot was blocked in a packed defence.
Armstrong finally brought a last-gasp save by Brown just under the crossbar following a near-post header when he thought he could have salvaged a point.