The diminutive winger struck in first-half stoppage-time to register his first goal since joining United in a loan exchange from Bristol City.
He opened his Colchester account in some style when seizing on a half-cleared corner and arrowing an angled drive through a crowd of players and past stranded keeper Mark Tyler.
It set Colchester on the way to a comfortable victory which has virtually ensured their League One status, but almost certainly deprived Posh of theirs.
Posh chief Barry Fry has vowed to step down as manager at the end of the current campaign but his successor will be inheriting a team plying their trade in the basement of English football.
The home side rarely threatened either side of a two-minute purple patch midway through the opening half and their fate was sealed by two killer goals from Colchester in the final quarter.
Veteran Posh forward Andy Clarke twice scampered into the danger area but two golden opportunities came to nothing. The first chance was lost when his selfish play prevented strike partner Calum Willock having an attempt at an open goal before Willock himself sliced a second opening horribly wide.
And Posh were punished for those pieces of ineffective attacking. Goodfellow made no mistake from the edge of the box to change the complexion of the game on the stroke of half-time and that strike knocked the stuffing out of the hosts.
Neil Danns was allowed to ghost into the box to convert a Sam Stockley cross 20 minutes from time before Marino Keith completed the rout from the spot seven minutes from time.