Goal-shy Brentford made two changes from the side that were heavily defeated at the weekend.
They gave a debut to on-loan striker Mickael Antoine-Curier, who is at Brentford on a month's loan from Nottingham Forest.
Colchester were without goalkeeper Bobby Bowry who was injured at Oldham last Saturday.
The home side's first real effort on target came on 21 minutes when Matt Somner's strike from 20 yards that was brilliantly saved by keeper Richard McKinneyBut the Bees did open the scoring on 37 minutes when Mickael Antoine-Curier broke clear in the box and his right-footed strike from an angle was destined for the back of the net until Mark McCammon chested the ball over the line from close range.
Five minutes from the break at the other end a 35-yard effort by Karl Duguid was easily saved by keeper Smith and a minute later a Morgan 20-yard effort was fingertipped away for a corner.
After the break, Colchester dominated and should have equalised on 52 minutes when a Keith cross from the left found its way to Duguid, but he fired over from a good position in the box.
On the hour mark a McGleesh strike from inside the box was saved low down by Smith.
The visitors almost equalised on 73 minutes when a corner from the left fell to substitute Thomas Pinault but his goalbound effort was brilliantly cleared off the line by Kevin O'Connor.
Seven minutes from time a corner from the left by Keith appeared to hit the hand of Bees captain Mike Dobson, but the referee awarded a dubious spot kick and Keith stepped up to convert easily.
The Bees ended their run of three successive league defeats and Colchester deserved to leave Griffin Park with at least a point.
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