The visitors were behind after only five minutes and later conceded two late goals on the way to going down to their seventh successive league defeat.
Defender Connolly gave Crawley the perfect start with the lead from close range.
A free-kick from Adams was headed down by Josh Simpson and Colchester goalkeeper Mark Cousins parried a goalbound effort from Clarke before Connolly tapped-in the rebound.
Leading goalscorer Clarke increased the lead 19 minutes from time by firing left-footed into the top corner from 17 yards after latching on to a hurried clearance from keeper Cousins.
Winger Adams sealed the Red Devils' comfortable victory with a clever chip from 18 yards two minutes from time following a through-ball from Hope Akpan.
Adams should have put Crawley 2-0 ahead early on when his shot from close in was cleared off the line and keeper Cousins went full length to turn away a 20-yard effort from Akpan midway through the first half.
Colchester enjoyed more possession as the interval approached and Anthony Wordsworth fired over following a one-two with Clinton Morrison.
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