Goals from Jamie Devitt and Michael Coulson had put the Mariners ahead on two occasions, only for Lee Bradbury and Liam Feeney to equalise for the visitors.
Bournemouth substitute Jeff Goulding was then sent off within a minute of his introduction and Chambers made the Cherries pay with his first goal for Grimsby.
The hosts went in front after 27 minutes, Devitt forcing home a rebound after Jean-Louis Akpa Akpro's left-footed strike had been palmed away by Shwan Jalal. But Bournemouth levelled three minutes before the break when
Brett Pitman's ball found Bradbury unmarked at the far post and he made no mistake with his header.
Coulson converted a Peter Sweeney corner to give Grimsby the lead for a second time in the 61st minute, but a blunder by Mariners goalkeeper Nick Colgan gifted Bournemouth an immediate equaliser by letting Feeney's weak shot slip through his legs and over the line.
Bournemouth sent on Goulding but he was on the pitch for less than 60 seconds before being dismissed for an apparent elbow on Jude Stirling. Chambers then popped up with the winner at the death, the striker converting Joe Widdowson's cross from close range.