Lee Harper's earlier own goal had handed Rochdale the lead, but Izale McLeod's 81st minute strike and Stanton's 87th minute gaffe ensured Dale caretaker boss Keith Hill got off to a losing start.
Rochdale started brightly and winger Joe Thompson perfectly teed up skipper Gary Jones inside the first minute, but his 22-yard strike flew straight into the grateful arms of Dons goalkeeper Harper.
The Dons looked strangely subdued as an attacking force early on as Dale defended well, with Izale McLeod's scuffed effort from a difficult angle the high-flying hosts' only chance of the first half.
The visitors continued to dominate possession and lone striker Glen Murray's towering far-post header from Alan Goodhall's cross was plucked out of the top corner by Harper in the 29th minute.
Milton Keynes upped the tempo after the break and Lloyd Dyer raced onto a long ball three minutes after the re-start but his 12-yard angled drive was saved well by Rochdale keeper Matthew Gilks.
At the other end, John Doolan smashed a decent 22-yard chance high over the bar before curling another 25-yard effort straight at Harper.
But Rochdale continued to press and Harper's unfortunate own goal handed them the lead in the 57th minute after the Dons could only half-clear a corner.
Harper initially punched the ball clear of the danger zone but it was recycled across to William Mocquet, whose low deflected 10-yard drive rebounded off the post and into the net off goalkeeper Harper's back.
The fired-up Dons battled back and the unmarked Aaron Wilbraham half-volleyed Jon-Paul McGovern's teasing free-kick wide from close range before Dyer drilled the ball into the side-netting from a difficult angle in the 72nd minute.
Dale threatened on the counter-attack and Callum Warburton almost made it 2-0 after turning Dons defender Paul Butler inside out, but his stinging 12-yard drive was saved well by the diving Harper in the 76th minute.
McLeod equalised for the Dons when he raced onto Wilbraham's flick and drilled low past Gilks from the edge of the box in the 81st minute.
Seven minutes later defender Stanton inadvertently poked substitute Scott Taylor's flick over his own keeper's head from 20 yards to give the home side the points and move them to second in the table.