Crawley threatened early on when the recalled Andy Drury drove a shot wide from the edge of the area.
Colchester goalkeeper Sam Walker was forced to save a low shot from Billy Clarke with his legs before smartly gathering a goal-bound effort from Jones, who should have hit the target when he shot across goal after a move involving skipper Josh Simpson and Mark Connolly.
The unmarked Drury failed to connect with a teasing cross from Clarke before Jones struck to put Crawley ahead after 41 minutes from close range after a clever lifted ball over the top by Clarke.
Colchester attempted to raise their game after the break and Craig Eastmond had a shot charged down before Sanchez Watt headed firmly against the crossbar from a David Wright cross.
U's manager Joe Dunne introduced much-travelled striker Clinton Morrison and Dominic Vose from the bench with 20 minutes remaining and Vose came close to equalising when he fired against the post with nine minutes remaining.