The League Two visitors were in the ascendancy from the moment that striker Aaron McLean headed them into a fourth-minute lead, with what was his 20th goal of a terrific campaign.
Even though they were pegged back by a soft penalty decision in the 43rd minute, from which Teddy Sheringham scored, Darren Ferguson's men did not let that prey on their minds and they eased through thanks to second-half goals by George Boyd and Charlie Lee.
It was a dreadfully disappointing performance from Colchester, who were never at the races. Posh bossed possession throughout and could have won by an even healthier margin.
An on-fire McLean deceived his marker Pat Baldwin to head home the opener from a corner by Jeff Hughes after four minutes, and only some heroics by keeper Dean Gerken kept the home side in the hunt.
Posh were even denied by the woodwork when McLean was thwarted again, and they were cursing their luck when the referee awarded the U's a penalty for an apparent push on striker Kevin Lisbie by Chris Whelpdale.
Sheringham made no mistake from the spot to chalk up his fourth goal of the season, but the U's could not make the most of their good fortune and they were trailing again within 26 seconds of the start of the second half.
The Essex club were caught cold as the excellent Lee swung over a cross for Boyd to lash home an angled drive.
Peterborough made the game safe in the 73rd minute when a corner by Whelpdale was headed clinically home by Lee. It was the perfect way for ex-Tottenham midfielder Lee to celebrate his 21st birthday.
Colchester rarely looked like finding a way back into the game, although substitute Karl Duguid forced a good late save from keeper Mark Tyler.
Otherwise, Tyler enjoyed a very quiet afternoon, leaving hapless Colchester to concentrate on their struggle against relegation.
On the day, it was Peterborough rather than Colchester who looked to be the Championship outfit.