Both sides began the day in the relegation places but the visitors came to Highbury knowing defeat would confirm their relegation to League Two.
And they were close to a victory that would have made Town's task all the harder over their remaining two games.
Luke McCormick’s excellent strike sent Wimbledon into half-time ahead and they spent most of the second period desperately clinging to their lead in a game high on tension but low on real quality.
And with two minutes left, a free-kick gave substitute Garner the chance to snatch a draw, firing in to send over 5,000 at a sun-soaked Highbury wild and virtually consign Wimbledon to League Two football.
Stephen Crainey brought back Danny Andrew, after seven games out with a hamstring injury. His only other change from the draw at Gillingham was the return of Anthony Pilkington, who came in for the suspended Paddy Lane.
Wimbledon boss Mark Bowen made one change – Anthony Hartigan replacing Alex Woodyard in midfield – from their Easter Monday game in his bid to register their first victory since early December.
The game’s first chance fell to Fleetwood, 14 minutes in. Andrew drove a ball goalwards and it fell kindly for Pilkington. He chose to shoot but a partial block by Dons skipper Ben Heneghan took the sting out of his effort and Nikola Tzanev made a comfortable save
An even better opening came Josh Harrop’s way moments later thanks to a through ball by Pilkington. Harrop should have at least made Tzanev work to keep the game goalless but he skewed his attempt well wide.
And Fleetwood were made to regret those misses when McCormick opened the scoring midway through the half.
It was perhaps the first time the visitors had passed their way into a meaningful attacking position, and when Jack Rudoni played in McCormick he side-footed a first-class finish into the top corner.
With Town struggling to exert any control over the remainder of the half, it was Wimbledon who went closer. Sam Cosgrove reacted well to beat Toto Nsiala to Lee Brown’s cross from the left but couldn’t direct his header goalwards.
After10 uneventful second-half minutes Hayes finally gave the sell-out Highbury fans something to get excited about .He collected Andrew’s long crossfield ball and turned William Nightingale before sending his shot just beyond the far post.
Twenty minutes from time, Crainey replaced Dan Butterworth, himself an early substitute for Ellis Harrison, to send on Garner, desperate for a flash of inspiration.
Garner’s goal changed everything, though, just ahead of nine added-on minutes that ramped up the tension to boiling point but produced no further goals.
Elsewhere, defeats for Gillingham and Morecambe – plus Town’s game in hand against Sheffield Wednesday – means their destiny is still in their own hands.
Feetwood:Cairns, Macadam, Nsiala, Jules, Andrew, Batty, Camps, Pilkington,Hayes, Harrison (Butterworth 19, Garner 72), Harrop (Morris 62); Subs not used: O'Hara, Biggins, Boyle, Bird.
Wimbledon:Tzanev,Kalambayi, Heneghan, Nightingale, Marsh, McCormick, Hartigan(Adjei-Hersey 90), Rudoni (Chislett 71), Brown, Cosgrove (Osei Yaw70), Assal; Subs not used: Lawrence, Awonkoya-Mdbude, Guinness-Walker, Broome. Referee:A Backhouse, Attendance; 5,019