Callum Wilson scored either side on half time for City, who deservedly took the points.
Boss Joe Dunne had to contend with the late withdrawal of Josh Thompson, and then lost Ryan Dickson through illness after twenty minutes.
He will have to assess injuries to a number of his squad this coming week, including Freddie Sears, Gavin Massey and Sanchez Watt.
Four changes were made to the starting eleven, with Marcus Bean, Drey Wright, David Wright and Jabo Ibehre coming in.
Not thirty seconds had been played, and the boss Joe Dunne must have thought he had a dilemma on his hands when Jabo Ibehre went down, but fortunately he was able to carry on.
Pacey winger Drey Wright won a free kick in a dangerous position when Christie brought him down. Dickson whipped a fantastic ball across the area, where Eastmond headed the ball back across the six yard box, but unfortunately no one got on the end of it and Coventry cleared their lines.
When Baker sent Fleck through, the U’s were put under pressure, when his looping cross found the head of Callum Wilson, who could only head into the grateful hands of Walker.
Wilson this time turned provider, as his low cross was perfectly weighted for the onrushing Leon Clarke, who directed the ball goalwards, forcing a fantastic save out of Sam Walker.
The U’s keeper was pivotal in the next chance for the home side, as Coventry once again broke down the right hand side, and Wilson put another ball across for Clarke, this time making Walker get down low to save with his feet.
It was all the home side with fifteen minutes played, as Christie weaved his way through Drey Wright and then Dickson, before shooting straight into the arms of Walker.
Eastmond won the U’s a corner on the break, Brian Wilson’s header was sent towards Murphy in goal for Coventry, before Gilbey got in front and diverted the header up and over the home side’s goal.
More problems for the U’s halfway through the first period as Dickson had to be replaced by Mason Spence, forcing Tosin Olufemi over to left back as Spence went to right back.
Baker got down the left again for Coventry, and lofted the ball near post for Clarke, who’s header found only the side netting.
Leon Clarke broke into the box, beat Wilson and his powerful shot rattled the bar, giving the U’s another first half scare.
With ten minutes of the first half to go, the U’s best chance of the game went begging as Ibehre flicked the ball into Gilbey, who dinked the ball over the defence, before blasting over from just ten yards.
This proved costly as just a minute later, Coventry were in front when Walker parried a shot straight into the path of Callum Wilson, who couldn’t miss as he tapped the ball into an open goal.
Coventry had the chance to double their lead just minutes later, when Moussa’s cross was looking ever likely to be headed goalwards by a Coventry player before Eastman intervened and flick the ball away for a throw.
The U’s made a change at half time, bringing on Clinton Morrison for David Wright.
They started the second half brightly with Wright and Olufemi linking up well down the right hand side, and attacking with good pace and width, winning corners, but not taking the chances very well, as Coventry managed to clear their lines every time.
Coventry doubled their lead in the 60th, when Callum Wilson managed to break free of the U’s defence, leaving Brian Wilson on the floor, before rounding the despairing Sam Walker and putting the ball into the empty goal.
Colchester made their final sub of the game, when Marcus Bean was replaced by Andy Bond for a straight swap in midfield, with an hour gone.
Coventry were attacking at a constant pace, with both Morrison and Ibehre looking increasingly isolated up front for the U’s, as they had very little to feed off with so much Coventry pressure.
He didn’t direct it though, and Sam Walker pushed the ball away with less than a quarter of an hour to play.
Clarke had a fantastic chance to make it three at the back post when Moussa’s searching cross evaded every U’s player in the area, allowing the Coventry forward to have a free header.
They made their second change soon after when Manset replaced goals scorer Wilson, with five minutes to play.
The last change of the match came in stoppage time, when Jordan Willis came on to replace Franck Moussa.