Second-half goals from Sam Baldock and substitute Angelo Balanta put the Dons 2-0 up before Lee Hughes pulled a goal back for County, who are now just two points above the relegation zone.
County started brightly and Alan Judge had a low shot well-saved by goalkeeper David Martin after sneaking in behind the Dons defence early on.
Dons settled into their passing game midway through the first half and Peter Leven curled a 25-yard free-kick inches wide, while Mike Edwards headed a good chance wide for County on the stroke of half-time. But the hosts upped the tempo after the break and Stuart Nelson tipped wide a long-range shot from Balanta before Baldock put them ahead, ramming in Leven's deep cross on the half-volley from close range.
Martin then produced two excellent saves to deny Karl Hawley an equaliser before Balanta doubled the Dons' lead in the 59th minute, poking in Baldock's low cross from three yards.
Hughes pulled a goal back for County three minutes later when he fired in from close range after Martin flapped at Craig Westcarr's corner but they were unable to force an equaliser despite some late pressure.