Saturday's victory climaxed a remarkable turnaround for the Cherries, who began the season with a 17-point deduction, and provoked a mass celebratory pitch invasion after the final whistle.
Fletcher's fairytale winning goal came 11 minutes from the end of an emotionally-charged relegation affair in front of a packed 9,000 crowd.
Grimsby, all but mathematically safe themselves despite the defeat, snatched a half-time lead through a Nathan Jarman header.
But, right on half-time, they were reduced to 10 men when Danny Boshell was sent off for a second bookable offence.
A minute into the second half Bournemouth equalised through Liam Feeney after Danny Hollands had hit the crossbar and Fletcher drilled home Bournemouth's winner 11 minutes from the end after a great run by Mark Molesley, before Joe Widdowson was sent off in stoppage time for a second yellow card.