Michail Antonio's first-half strike was enough to give Colchester all three points at Chesterfield.
After the hosts could only half clear a corner, Antonio made no mistake from the edge of the area with a low drive.
Alex Mendy drew a fine save from visiting keeper Ben Williams before Leon Clarke saw a shot come back off the post as the Spireites pushed on.
Clarke saw another effort go just wide before having a late penalty shout waved away.
VIEWS FROM THE DRESSING ROOM
Chesterfield manager John Sheridan told BBC Radio Sheffield:
"There were a lot of positives for me, I thought we played really well.
"It's a very poor goal on our behalf but full credit to the players.
"I thought we had great opportunities to get back in the game. On another day we could have scored four or five goals. It's a shame for their efforts we didn't get anything out of the game, because I don't think we deserved that."