Bradford, chasing a play-off place, went ahead when Wes Thomas converted Josh Cullen's pass, but Kevin Keen's side levelled through Ambrose's volley.
Buoyed by the leveller, George Moncur struck an upright, before Ambrose took Owen Garvan's pass to make it 2-1.
It was enough to secure a double against the Bantams this season.
The win was Colchester's first in League One since a 2-1 home success against Port Vale in October, and Keen's first in the competition since his December appointment.
Phil Parkinson's side dropped two places to ninth after the defeat, their first in five.

That was just over over half of last year's haul, when the website auctioned a coffee meeting with the Apple boss.
The money will benefit the Robert F Kennedy Center for Justice and Human Rights.
CharityBuzz declined to reveal the winner, who will get a one-hour lunch with Mr Cook at Apple headquarters (cost of travel not included).
Mr Cook also added a second prize on Twitter, which will give the winner a VIP seat at an upcoming Apple event.
CharityBuzz had estimated the value of the lunch date at around $100,000.
Part of the reason for the lower price tag could be that CharityBuzz implemented a finance authorisation requirement for anyone wishing to bid on the auction.
But while appetite for a bite with Mr Cook may have cooled (or Silicon Valley lovers might just prefer a well-brewed cup of coffee), his stock, much like Apple's, remains high.
An auction for a similar lunch date with former Federal Reserve chairman Ben Bernanke took in just over $70,000, and a still-open auction for a coffee date with AOL boss Tim Armstrong - which also includes a tour of HuffingtonPost Live and a taped interview - currently has zero bids.
Warren Buffett, chief executive of Berkshire Hathaway, was one of the first to popularise a "lunch with the boss"-style charity auction 14 years ago.
Last year, lunch with the "oracle of Omaha" sold for more than $1m on eBay, off the record $3.5m winning bid in 2012.
Darren Ambrose's double helped struggling Colchester United come from behind to win 2-1 at Bradford City and end a 19-game League One winless run.
[NEXT_CONCEPT]
A lunch date with Tim Cook has sold for close to $330,000 (£196,000) on the auction website CharityBuzz.