Danny Wilson's Dons had looked to be on course for their third victory of the season after dominating the first half and despite the win they remain rooted to the bottom of the League One table.
Blackpool went ahead after just 17 minutes when Simon Grayson was tripped by Nicholas Rizzo as he burst into the box and skipper Peter Clarke stepped up to convert the spot-kick.
But just two minutes later the roles were reversed when Clarke himself brought down winger Wade Small and Rizzo steeped up to score the penalty.
Small, returning after injury, was a constant menace on the right wing and put his side ahead after 34 minutes with a lobbed shot from the right-hand side of the area before he was taken off at half time with a dead leg.
Blackpool took just five minutes of the second half to get back on terms when young winger Jamie Burns put in a cross that Mills should have dealt with easily.
But instead of putting the ball behind, the big defender, on loan from Derby County, inexplicably chose to head it past keeper Matt Baker and into his own net.
Blackpool's half-time substitute Keigan Parker was a constant menace and carved out what proved to be the winning goal with 22 minutes remaining.
His cross from the right-hand edge of the area missed his strike-partner Tommy Wright but fell kindly for youngster Jamie Burns to finish clinically from 12 yards out.
MK Dons showed plenty of creativity at the other end of the park with striker Izale McLeod always a threatening presence.
Clarke had to clear off his own line on a couple of occasions while big keeper Les Pogliacomi also had to stretch to deny McLeod in the closing stages.