Dyer's brace and substitute Scott Taylor's cool finish had put the Dons 3-0 up at the National Hockey Stadium.
But late strikes from County's Jason Lee and Dan Martin made it a tense finish, despite Matt Somner and Alan White having seen red for the visitors.
Dons manager Martin Allen made two changes to the team that won 1-0 at Boston last Saturday with new skipper Keith Andrews - signed from Hull on a free transfer this week - making his debut in centre midfield alongside the recalled Gary Smith.
Craig Morgan was absent on Wales international duty, while Izale McLeod started the first game of his three-match ban after his red card for stamping.
County thought they had earned a penalty just six minutes in after Drissa Diallo pulled down Lee in the box, but after awarding the spot-kick referee Danny McDermid saw the linesman's flag for offside and instead gave the Dons a free-kick.
Dan Martin forced Dons goalkeeper Adolfo Baines into a decent low save with a curling 25-yard free-kick on the quarter of an hour mark, after Sean O'Hanlon was adjudged to have handled Martin's well-struck long range drive.
Martin continued to impress for the visitors and his sweetly struck half-volley from 12 yards was superbly saved by Baines at his near post midway through the first half, before Martin's inswinging corner almost caught out the Dons stopper, but it hit the top of the bar and went over.
But County's hopes were dealt a blow when tough-tackling midfielder Somner was sent off for a rash tackle on Dean Lewington just after the half hour mark - his second bookable offence.
And Dyer made him pay a minute before the break when he drilled in a free-kick to put the Dons 1-0 up, after Austin McCann's poor backpass was handled by Magpies' keeper Kevin Pilkington as it was flying over his head towards the net.
Jon-Paul McGovern touched the ball off and Dyer hammered it low through the wall of County defenders into the bottom corner from 12 yards.
As the Dons began to pile on the pressure, County's hopes of getting back into the game all but vanished when they were reduced to nine men in the 60th minute, after skipper White picked up his second booking for a foul on Dyer.
And Dyer capped a superb individual display by completing his brace with a deflected angled drive to make it 2-0 in the 53rd minute.
McGovern played a short corner to Dyer, whose inswinging low strike deflected off the unfortunate Lee and past the helpless Pilkington.
Substitute Taylor made it 3-0 in the 73rd minute when shrugged off Magpies midfielder David Pipe to latch on to McGovern's through ball before coolly slotting under Pilkington.
But Lee pulled a goal back for spirited County in the 77th minute, ramming in from close range after a goalmouth scramble in the Dons' box.
And Martin's 25-yard free-kick went straight through Dons goalkeeper Baines' hands to make it 3-2 six minutes from the end, but Milton Keynes hung on against the battling nine men of County.