Wolves had raced into a 3-0 half-time lead only to then have to hang on for the three points.
Michael Jacobs broke the deadlock after just 50 seconds before Dave Edwards and James Henry increased the home side's advantage.
But Alex Gilbey - with Colchester's first ever goal at Molineux on their sixth visit - and David Wright then set the alarm bells ringing for Wolves before Freddie Sears hit the post for Colchester.
Nouha Dicko finally ended Colchester's comeback hopes with a strike in the fifth minute of stoppage time.
Jacobs opened the scoring when his left-wing cross deceived everyone and left goalkeeper Sam Walker flat-footed as the ball nestled in the corner of the net.
Edwards strengthened Wolves' advantage in the 27th minute when he latched on to a mis-placed back pass from Ryan Dickson to take the ball around Walker before rolling it into an unguarded goal.
Henry then underlined Wolves' first-half supremacy two minutes before the interval when Walker tipped away Leon Clarke's shot only to see Henry turn home the rebound.
But Colchester were a different proposition in the second-half and Gilbey nodded home a cross from Dominic Vose after 52 minutes.
Any hopes that Wolves had of coasting to victory were then dashed by Wright, who volleyed Sears' cross into the net from inside the six-yard box in the 71st minute.
Sears then beat Ikeme with a low drive six minutes from time only to see the ball crash off the foot of the post.
But as Colchester pressed for an equaliser, Dicko was able to use his pace to race clear and score from an acute angle.