Yet it was the visitors who enjoyed a dream start when they took the lead after only eight minutes.
Right-back Little did the spadework, bursting down the flank and pulling the ball back to Nathaniel Mendez-Laing, whose shot was parried by Dons keeper David Martin straight into the path of Mackail-Smith who could not miss.
It was the striker's 33rd goal of the season, and he soon went close to number 34 as he fired an angled drive over the bar after taking a Mendez-Laing pass in his stride.
Lee Tomlin also forced a smart save from Martin before the Dons finally came into the game in the run-up to half-time.
It was the unlikely figure of defender Mathias Doumbe who went close to an equaliser three times, first forcing a fine reaction save out of Joe Lewis with a header before seeing a low drive deflected over the bar by Kelvin Langmead and a third effort turned on to the outside of a post by a defender.
Posh were forced into a half-time reshuffle, with Paul Jones coming on in goal in place of Lewis, who had needed treatment early in the first half following a collision with Lee.
But Jones endured a first 10 minutes to forget as he picked the ball out of his net three times.
First he failed to deal with Tommy Rowe's mis-directed defensive header, allowing Powell to stab in the equaliser from close range.
He was helpless to prevent the second when Baldock's speculative low free-kick flew through the Posh wall and into the net, and the third when Balanta seized on Adam Clayton's pass, slipped inside a challenge and drove past Jones at his near post.
Peterborough were even more up against it when left-back Lee was shown his second yellow card for a foul on Powell, and could have been out of the tie had Baldock not dragged a shot wide.
But they were handed a lifeline when Gleeson was harshly dismissed for tripping the marauding Little, and McCann made no mistake from the spot.
MK Dons manager Karl Robinson told BBC Three Counties Radio:
"I'm proud of them, I'm so proud of them.
"All my pre-match build-up was saying 'I promise we won't let you down, we might lose the game or the tie but it will never be through a lack of hard work, it may be something that goes against us where we're unlucky'.
"Today we had a lack of luck, but we've come through it the other side. Everything's gone against us, yet we're still 3-2 up."
Peterborough United manager Darren Ferguson told BBC Radio Cambridgeshire:
"The performance was probably as bad as we could have played in a game like this.
"I've just told them the same, I've not told them anything different.
"It's the wrong day to pick to have such a poor performance, particularly on the ball.
"Milton Keynes were far better than us on the day, I'm delighted to still be in the tie."
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