The Dons seemed to be coasting to victory when U's goalkeeper Aidan Davison was sent off for lashing out at Izale McLeod in the 69th minute, after Aaron Wilbraham had deservedly broken the deadlock.
But centre-half Chilvers rose highest to head home Neil Danns' corner 11 minutes from the end to rescue a point for the visitors.
Dons' boss Danny Wilson made four changes to the team that lost 2-0 at Bradford, with new-boy Trent McClenahan replacing Shola Oyedele at right-back and 18-year-old Nick McKoy making his first start of the season at the expense of Gary Smith in centre-midfield.
Veteran Steve Palmer came in for suspended skipper Ben Chorley, with Dean Lewington taking the captain's armband after Paul Mitchell missed out with a recurrence of his knee injury, and Jason Puncheon named on the left of midfield.
Colchester manager Phil Parkinson stuck with the same eleven that won 1-0 at Barnsley.
The U's were quickest out of the blocks and Kem Izzet stung Dons' goalkeeper Matt Baker's fingers with a firm shot on the turn from Wayne Brown's cross.
But just moments later Dons' hit-man McLeod raced onto Wilbraham's flick and crashed a fierce strike off the crossbar, before Jason Puncheon volleyed the follow-up wide.
Milton Keynes began to take control and Palmer should have given them the lead in the 17th minute when Puncheon's free-kick found him unmarked five yards out, but he somehow failed to get a touch.
But just six minutes later the Dons took a deserved lead thanks to Wilbraham's well-struck volley, after Pat Baldwin's poor defensive header fell kindly for him to open his account for the club from 12 yards.
Milton Keynes came out fired up after the interval and Puncheon and Small both came close before the unlucky McLeod rattled the bar again after a scintillating run.
Wilbraham was then denied his second of the match by a fine stop from Davison, after Edds had slotted him through on the right.
At the other end, Chris Iwelumo's header from five yards was spectacularly scooped round the post by Baker, before the Dons' stopper was again on hand to tip round Mark Yeates' 25-yard strike.
The visitors' hopes of getting back in the game seemed slim when Davison was sent off in the 69th minute for lashing out at McLeod as the players jostled for position at a corner.
But 10 minutes later the U's were level when Chilvers powerfully headed home Danns' flicked on corner.