Fleetwood led in London through Ged Garner’s seventh goal of the season.
But Crainey’s tenure looked like it was destined to begin with defeat as the hosts turned the tables through goals from Ayoub Assal and Luke McCormick.
But Callum Johnson clinched a credible point for their vocal travelling supporters.
The interim boss made two changes after Tuesday’s desperately disappointing defeat at Covid-hit Oxford.
One was enforced as injured Joe Garner was replaced by Shayden Morris and Harrison Holgate came in for Max Clark.
Fleetwood’s 3-1 defeat at the Kassam was the final straw as a torrid run of results finally caught up with Grayson.
Grayson picked up a paltry eight points from his final 12 league games in charge of the struggling Lancashire club.
Fleetwood started brightly, with the fans who made the treacherous 267-mile trip down to the capital in full voice.
Towering forward Callum Morton couldn’t quite get on the end of Callum Johnson’s teasing cross.
Jay Matete fired over the hosts’ bar as he let rip from outside the box.
Morton saw an effort rightfully chalked off for offside as the visitors thought they had claimed a vital lead.
But the Lancashire outfit got their deserved lead 10 minutes before half-time as Garner’s super strike broke the deadlock.
And Johnson tried to replicate his teammate’s heroics when he blasted just over the bar after shouts of “shoot” from the away end.
The Dons squandered a glorious chance to level in first-half stoppage time as Ollie Palmer, who bagged a brace last time out, got tangled up at close range.
Crainey’s charges missed a gaping chance to go two up minutes into the second half.
Morton once again couldn’t quite reach Morris’ cross with the goal at his mercy.
And that missed opportunity came back to haunt the visitors as Wimbledon equalised.
Assal, who had his Tuesday-night sending-off overturned, levelled with a fine finish.
And Wimbledon had their tails up as Fleetwood struggled to clear their lines for sustained periods due to the strong winds in South London.
But Dons stopper Nik Tzanev was forced into a couple of quickfire saves to keep the game level.
Danny Andrew headed at the shot-stopper before requiring treatment as he went down clutching his face.
And the Kiwi keeper made an even better save to deny Morton with just over 20 minutes remaining.
The Cod Army’s woes got worse as Holgate was stretchered off and minutes later Andrew went off injured.
And McCormick struck with 11 minutes to go to seemingly send Fleetwood to another frustrating defeat.
But Johnson salvaged a precious point with six minutes to go.
Fleetwood had the best stoppage-time chances through substitutes Stephen McLaughlin and Ryan Edmondson.
AFC Wimbledon: Tzanev, Osew (Lawrence, 69), Heneghan, Csôka, Guinness-Walker, Woodyard, Hartigan, Assal, McCormick (Chislett, 85), Rudoni, Palmer (Pressley, 85).
Unused subs: Jenkins, Marsh, Awokoya-Mebude, Oualah.
Fleetwood: Cairns, Johnson, Clarke, Holgate (McLaughlin, 71), Andrew (Biggins, 73), Lane, Batty, Matete, Morris (Edmondson, 89), Garner, Morton.
Unused subs: Crellin, Clark, Johnston, Boyle.
Referee: Robert Madley
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