The game began with both teams going through the motions, the first chance coming in the seventh minute courtesy of Michael Bostwick's shot from outside the area, which was blocked.
Just over a minute later, Dominic Vose attempted an effort from a difficult angle, which whistled just past the post, while on the quarter-hour mark, Colchester's Grant McCann saw his long-range shot rebound off the left post.
Midway through the first half, however, Tommy Rowe managed to break the deadlock for the home side, thanks to a downward header from a corner which nestled into the bottom right of the goal.
The start of the second period, much like the opening stages of the first half, was a slow affair, but the impasse was broken in the 54th minute when Danny Swanson fired from the right-hand side of the box. His shot for the Posh was just wide, however.
The U's, under the cosh for much of the game, had a rare chance on goal when David Wright fired over from outside the box, but any hopes of a comeback were soon put to bed when the home side doubled their lead just after the hour, Britt Assombalonga tucking the ball into the bottom left corner of the U's goal.