Goals from Clive Platt and Keith Andrews saw the Hatters beaten at Edgeley Park, although Anthony Pilkington's 80th-minute strike gave his side hope.
But with just two fixtures left in League Two, Jim Gannon's hopefuls still have work to do in their bid to challenge for promotion.
Martin Allen's Dons deserved the points and renewed their faint hopes of catching third-placed Swindon in the table, their rivals who have the advantage in the race for automatic promotion.
Pilkington missed an excellent chance to give the home side the lead in the 23rd minute, but he blazed over the bar and Hatters were punished when Platt beat his marker to fire a powerful shot past keeper Joe Lewis.
And it got even better for the visitors when Andrews rose tallest to double Dons' lead in the 55th minute, a goal which left Gannon's men deflated.
To their credit, Stockport battled bravely and when Pilkington netted ten minutes from time, beating Dons keeper Ademole Bankole with a fierce drive, there was hope of a point.
But Dons held on and can still catch Swindon in their bid to avoid the play-offs and go straight up so long as they win their remaining games and their rivals their two remaining fixtures.