City have not won a league game since March and paid for a lacklustre first-half display which saw the visitors grab the lead after half an hour through Matt Taylor's powerful header from a Luke Garbutt cross.
Colchester themselves have now not won for seven games and Baldock rewarded a vastly improved second-half display from the hosts by shooting home a right-foot shot at the far post from a low Stephen McLaughlin cross.
Baldock could have won it for Sean O'Driscoll's team late on but headed wide from another McLaughlin cross, while at the other end Jabo Ibehre broke clear only to be denied by goal-saving tackle from Derrick Williams.
City improved after the introduction of veteran striker Marlon Harewood as a 53rd-minute substitute for midfielder Bobby Reid.
But Colchester withstood the bombardment, with centre-back Magnus Okuonghae outstanding at the heart of their defence.