Gary Smith's first-half penalty looked to have put the Dons on course for a much-needed victory, but Darren Byfield's crisp angled drive and Tommy Black's cheeky free-kick condemned them to their third straight defeat.
Gillingham dominated the first quarter of an hour but despite forcing a succession of corners, all they had to show for their efforts was Byfield's long-range strike that Dons goalkeeper Ricardo Batista saved comfortably.
The Dons, playing against a gale force wind, gradually battled their way into the game and Smith's fierce low strike from the edge of the box was saved well by Gills' keeper Jason Brown in the 17th minute before Filipe Morais blasted over when well placed.
Alan Pouton lashed a 25-yard half-volley just over the bar in the 26th minute for the Gills, before Smith put the Dons ahead from the penalty spot at the other end in the 40th minute.
Izale McLeod was barged over in the box by Gills' full-back Jon Wallis near the by-line after latching on to Nicky Rizzo's through ball, and Smith stepped up to calmly send Brown the wrong way from the spot.
Byfield almost equalised for the Gills on the stroke of half-time but his close-range header from Black's pin-point cross was acrobatically tipped over the bar by Batista.
Byfield went close again three minutes after the re-start when he headed just wide from nine yards after the Dons' defence allowed a long throw to bounce in the box.
The Dons settled into their stride and they could have made it 2-0 when Clive Platt's header was pushed wide by Brown, Nicky Rizzo curled an effort just wide from 22 yards and then Morais' cross-shot hit the top of the bar in the 53rd minute.
But they were made to rue those misses when two quick goals in two minutes from Gillingham's Byfield and Black turned the game on its head.
Byfield collected the ball on the left before surging towards goal, and as Dons' defender Ben Chorley continued to back off, he fired low left-footed across Batista into the corner in the 60th minute.
Then after Dons skipper Paul Mitchell had brought down Andrew Crofts on the edge of the box, Black caught keeper Batista napping by clipping a quick free-kick into the net as he was lining up his wall in the 62nd minute.
McLeod almost gave the Dons the perfect response from the re-start but after controlling Smith's lofted through ball, his close-range strike was tipped over the bar by Brown.
Smith's deflected long-range drive was saved well by Brown in the 83rd minute as the shell-shocked Dons searched for an equaliser, but it was Gillingham who came closest to adding to their tally when substitute Danny Spiller clipped Wallis' cross wide from close range a minute from the end.