United pulled two back through Alex Gilbey and David Wright in the second half, but they were not to be the foundations of a miraculous comeback as Nouha Dicko put the result beyond doubt in the dying stages.
Jackett could hardly have wished for a better start after a Jacobs cross flew past goalkeeper Sam Walker and nestled in the far corner after two minutes.
Henry, who has bagged a goal in each of his previous two outings, failed in a one-on-one with Walker before Wanderers' pressure paid dividends.
The West Midlands outfit doubled their advantage shortly before the half-hour mark through Edwards, who capitalised on a loose backpass from Ryan Dickson before rounding the helpless Walker and tapping into an empty net.
Henry trebled his team's lead shortly before the half-time whistle by firing home a rebound to score in his third successive fixture and give his team a seemingly unassailable advantage.
However, Gilbey was on hand to reduce the arrears with a powerful header on 58 minutes before Wright thumped home the second to give Colchester a glimmer of hope.
Gilbey saw his would-be equaliser smash off the post in the closing stages of normal time before Dicko converted a Bakary Sako cross shortly after to seal the 4-2 win.