Kenny Jackett's side looked in control in their first-ever meeting with the West Sussex club as Bjorn Sigurdarson netted in the seventh minute with the visitors proving wasteful in front of goal for large parts.
Crawley looked to have snatched a point in the 91st minute, though, Billy Clarke netting via the post from Jamie Proctor's cut-back.
However, the home fans went home happy as Kyle McFadzean was adjudged to have handled Kevin McDonald's cross.
Having conceded 13 goals in their opening three games, it was a surprise that the Cumbrians took the lead in just the fourth minute at the Weston Homes Community Stadium.
Matt Robson, who had tested Sam Walker in Colchester's goal with an earlier effort, broke the deadlock early on with a left-footed finish across the goalkeeper.
Colchester peppered the goal as they sought a way back into the game, and were finally rewarded with 20 minutes remaining as Freddie Sears got on the end of Gavin Massey's ball to equalise.
