The game only came to life five minutes into the second half when Mark Jones was gifted the lead for Wrexham. The midfielder's tame shot from 15 yards seemed no problem but keeper Dean Gerken somehow fumbled the ball and it rolled into his net.
Colchester hit back with two goals, both from corners, to deservedly take the lead. The first was a Neil Danns header after an effort from Greg Halford was blocked on the line following Kevin Watson's flag kick.
Home goalkeeper Ben Foster was too keen in going for Watson's next dangerous corner, causing confusion in his own defence.
Danns was again in the action after 71 minutes and saw a header blocked on the line but Wayne Brown planted the rebound beyond Foster.
Wrexham manager Denis Smith sent on two substitutes to pep up the game when staring defeat in the face. It paid off when Hector Sam scored with a header to give the Red Dragons a point they hardly deserved.
Gavin Johnson had an early angled shot saved by Foster at the second attempt and the Wrexham keeper also held a short-range header from Stephen Hunt.
Craig Fagan also tested the goalkeeper on half-time but Foster denied him with a diving save.
Dennis Lawrence was denied by Gerken, who also saved a poor effort from Alex Smith.