Moussa, Edjenguele and McGoldrick give Sky Blues a third consecutive away league win
Coventry City made it 12 points from the last 15 with another impressive away win at Colchester United to move them up to 15th in the league table.
Franck Moussa netted his second goal in as many games with the opener after 34 minutes with William Edjenguele opening his account for the club with a header three minutes later.
Colchester gave themselves some hope with a glancing header from Tom Eastman with 20 minutes to go but David McGoldrick sealed the points with his 13th goal of the season with three minutes to go.
Unsurprisingly, boss Mark Robins opted to stick with the side that beat Hartlepool 5-0 at Victoria Park on Saturday and they appeared to pick up where they left off as they dominated possession in the opening ten minutes.
It was the home side that registered the first effort at goal though after 12 minutes when Anthony Wordsworth sent a stinging drive from 25 yards just over City 'keeper Joe Murphy's crossbar.
It was the Sky Blues who registered the first effort on target after 18 minutes though when a floated cross from the left from David McGoldrick found Franck Moussa at the back post whose header was only kept out by a last-ditch on-the-line save from John Sullivan.
Murphy was required at the other end three minutes later though when a crossfield ball caught Blair Adams out of position at left back and found Ian Henderson who rolled a ball back into the path of Brian Wilson whose shot from 12 yards was parried and then collected.
Colchester then thought they'd taken the lead after 29 minutes when Craig Eastmond's shot from 20 yards took a deflection off Marcus Bean and trickled into the net only for the goal to be ruled out for offside by referee Trevor Kettle.
The U's went close again just a minute later though when former Sky Blues loanee Freddie Sears picked up a ball on the corner of the City area and curled an effort just over Murphy only to see it crash off the crossbar.
City then took the lead after 34 minutes thanks to a superb piece of play.
McGoldrick played a fantastic through ball to pick out Gary McSheffrey intelligent run, McSheffrey then cutting across goal for Moussa to make a simple finish from three yards out.
Moussa nearly turned from scorer to provider seconds later when he crossed from the left for McGoldrick who volleyed an effort which Sullivan had to parry.
It was 2-0 to City though after 37 minutes amid confusion and fury from the home side.
Baker curled in a deep cross from the right which found Edjenguele to head downwards and into the net.
The assistant referee raised his flag for an incident which delayed Kettle's decision to award the goal, something he did after consulting his assistant much to the displeasure of the Colchester players who surrounded the referee in protest but only ended up with a yellow card for skipper Wordsworth.
The Sky Blues came out for the second half clearly buoyed by their performance in the first 45 minutes and they went close from a well worked set piece on 51 minutes when Steven Jennings cut a quick free kick from the left side of the area back for McGoldrick whose initial shot was blocked from 12 yards, the striker then slicing his follow up over the bar.
James Bailey then nearly carved the Colchester back four open with a great quick pass on the turn for McGoldrick who beat the offside trap but could not bend his shot from a tight angle beyond the reach of Sullivan two minutes after the hour.
Colchester got one back after 71 minutes though as they tried to turn the tide on the game, Wordsworth swinging in a free kick from the right which found Eastman to glance a header past Joe Murphy.
Murphy then had to produce an outstanding save with six minutes to go to keep City ahead when Wilson's diving header at the backpost looked certain for the net until Murphy managed to palm it away at full strength.
With the tension building as Colchester tried to make their momentum count the Sky Blues then put the game to bed with a swift counter-attack with 87 minutes.
Substitute Adam Barton slipped a perfectly weighted through ball for McGoldrick who beat the offside trap to slot past Sullivan.
City were still not satisfied though and continued to press as the fourth official showed four minutes of added time.
First Moussa twisted and turned his marker before shooting at goal and forcing a good save out of Sullivan.
Baker then went agonisingly close straight after with an effort from 20 yards which flashed just past the foot of the far post.
It was a fitting way for City to end the game though as the referee blew for full time to give the Sky Blues a third consecutive away win.
Attendance: 3,229 (408 Sky Blue Army)
Teams
CoventryCity: Murphy, Adams, Wood, Edjenguele, Christie, Bailey, Moussa, Baker (c), Jennings, McGoldrick, McSheffrey (Barton 77)
Subs: Dunn (GK), Clarke, Cameron, Fleck, McDonald, O'Donovan
ColchesterUtd: Sullivan, Rose, Okuonghae, Sears, Ibehre, Bean (Massey 45), Henderson (Morrison 62), Eastman, Wilson, Wordsworth, Eastmond (Bond 83)
Subs: Cousins (GK), Duguid, White, Thompson
Bookings: Wordsworth (COL), Henderson (COL), Morrison (COL), McGoldrick (COV), McSheffrey (COV), Jennings (COV)
Referee: T Kettle
AssistantReferees: D Rock, E Kaye
FourthOfficial: W Norcott