The home side took the lead as Macauley Bonne scored his hot scoring streak, but the Sky Blues showed why they're among the promotion contenders with a resolute display.
On a wet and dreary afternoon at the Weston Homes Community Stadium, Coventry City continued their strong start to the season to inflict a rare home defeat on the U's.
It was 17 minutes in when Joe Edwards ventured across the pitch from right back and found Callum Harriott on the left, he then delivered an inch perfect for in-form Macauley Bonne to deftly flick the ball in to make it 1-0 to the U's.
They had another half chance not long afterwards, but Jim O'Brien could only hit the side netting from the angle and Colchester made them pay.
Coventry were quick to start and would have been ahead after just three minutes if it wasn't for an excellent sliding tackle from Tom Eastman to deny Ruben Lameiras from scoring.
Moments later, an excellent counter involving Marvin Sordell, Moncur and Harriott but Harriott's chipped cross just failed to pick anyone out.
Marc Antoine Fortune delivered a cross from the left and Eastman appeared to have cut it out brilliantly, but it fell to Murphy to slot the ball home.
Coventry completed the turnaround on the 40 minute mark as Murphy got his second of the game.
A lapse in concentration at the back for the U's allowed Murphy to get on the end of a quick free kick, and although the home crowd appealed for offside, he rounded the goalkeeper and slot into the empty net.
The conditions certainly played a part as a shot from Lameiras from the right skipped up at Jamie Jones and the rebound fell to Antoine fortune to tap the ball into the empty net.
He placed a shot towards the bottom left corner, but it was saved smartly by Charles-Cook and he then produced a very good save from sub Gavin Massey on the rebound.