The Lions were second best for most of the evening, but they made the most of two errors from the home team inside the first quarter of the game and then held on to strengthen their promotion push.
Having weathered the early storm, the visitors grabbed the lead after nine minutes when Lewis Grabban made the most of a stray pass from home midfielder David Perkins, which had been meant for Johnnie Jackson.
Flying winger Grabban intervened and advanced a few yards before calmly sweeping his shot low past keeper Dean Gerken.
Another lapse in concentration enabled the Londoners to double their lead in the 23rd minute.
Midfielder Marc Laird swung over a deep free-kick to the far post for defender Paul Robinson to head home from close range.
Colchester were still waiting to record their first win at their new Community Stadium but they did come storming back and count themselves unlucky not to have at least secured a point.
Kemal Izzet halved the deficit in the 35th minute when he drilled home from eight yards out after Clive Platt had flicked on a cross from John White.
It was one-way traffic for most of the second half and Izzet thought that he'd grabbed an equaliser on 56 minutes.
His deflected cross cannoned back off the underside of the bar and dropped onto the goalline before it was hastily cleared. There was a suspicion of handball in this clearance.
Platt went close with two headers but Millwall defended well and gave good protection to their keeper David Forde.
There was one more clear-cut chance deep in injury time when Perkins almost made amends for his earlier error with a cross to the far post where sub Scott Vernon was within a whisker of diverting home.
The U's have now failed to win any of their first six home games since their summer move from Layer Road.