Freddie Sears slid the U's in front after just six minutes, stroking home a low cross from the right by Brian Wilson.
But Crawley grabbed a deserved leveller just after the half-hour mark when Emile Sinclair powerfully headed home Nicky Adams' cross.
Both sides had other chances during an enjoyable Sky Bet League One contest.
Jeffrey Monakana had an effort deflected wide and then powered a volley into the side-netting.
Jabo Ibehre then struck the crossbar after being teed up by Sears.
Alex Gilbey had Colchester's other best chance of note, but his shot from Monakana's cross deflected off Josh Simpson and into goalkeeper Paul Jones' arms.
Crawley also went close, especially in the seconds after their equaliser when Andy Drury hit the post and Billy Clarke's follow-up was well-saved by Sam Walker.
Wright then twisted inside David Wright, but saw his effort held by the U's keeper.
And Clarke went close again, stabbing home from close-range - only for his effort to be chalked off for offside.