Goals from Dean Lewington and Gareth Edds put the Dons in charge, before Keith Briggs pulled a goal back for the visitors, who had John Hardiker sent off 11 minutes from the end.
Stockport had marginally the better of the opening exchanges and Warren Feeney almost took advantage of a poor backpass just six minutes in, but Dons keeper Matt Baker was quick enough off his line to block at his feet.
The Dons fought back and when Ben Harding's fierce long-range effort was saved well by James Spencer in the County goal and Izale McLeod's attempts to fire in the rebound were thwarted by skipper Jim Goodwin's last-gasp challenge.
And as Milton Keynes Dons began to take control of the match with some free flowing football, they were gifted the lead in the 34th minute after a blunder from Stockport keeper Spencer.
Youngster Leon Crooks broke quickly to the byline and, when Spencer failed to hold his outswinging cross, Lewington was on hand to bag his third of the season from seven yards.
Lewington's mood took a turn for the worse six minutes later, though, when he was booked for diving in the box. But the Dons continued to press and after Edds had come close with a long-range effort three minutes after the break, Lewington should have had his second of the game but fired at Spencer when he was well placed.
McLeod then wasted another chance before Edds made the Dons domination count by driving in the second in the 59th minute after the ball fell sweetly on the edge of the box.
Feeney missed a golden opportunity to get Stockport back in the game seven minutes later when he somehow headed over from just two yards out.
Briggs did pull a goal back in the 73rd minute, driving in the rebound from an angle with Dons keeper Baker still out of position from blocking his first effort.
The Hatters hopes of getting back in the game went when Hardiker was sent off for a rash challenge on Lewington in the 80th minute, his second bookable offence.