The visitors took a ninth-minute lead when Sean Clohessy got the better of Greg Cunningham on the right and squared the ball for George Moncur to score with a low right-footed shot from 12 yards.
City hit back less than a minute after the break when Cunningham's low cross from the left was cleverly converted by Wilbraham with a deft right-footed finish that nestled in the far corner.
The striker was on target again in the 68th minute, rising at the near post to nod home as goalkeeper Sam Walker came off his line without reaching Wade Elliott's cross.
City only forced one save of note from Walker in the first half when Wilbraham's downward header from an Elliott chip lacked the pace to beat the Colchester goalkeeper after 16 minutes.
The home side were fortunate not to go two goals down in the 35th minute when City keeper Frank Fielding was caught out of position and U's striker Jabo Ibehre's chip from the right was just too high.