Jordan Spence got one back for the Dons early in the second half but substitute Macauley Bonne struck 12 minutes from the end to give Colchester just their second win in 18 games.
"It was a tremendous effort by all of the players. We've worked hard and I'm pleased for them because they've earned it," said Dunne.
"I want them to enjoy it and it's great because we've been grinding out results.
"Overall it was a very pleasing result and very workmanlike and we should have scored more goals."
- Sports & Recreation