Peter Halmosi gave Plymouth the lead in the first half when he raced on to Sylvan Ebanks-Blake's ball and slipped his shot past Casper Ankergren.
David Healy levelled just before the break, pouncing on the loose ball inside the area.
And Michalik scored the winner when he headed in Alan Thompson's free-kick.
Leeds assistant manager Gus Poyet:
"It's a great day. The last five games have been fantastic. I don't know how many months we've been there. "We're feeling great and enjoying it but unfortunately you cannot enjoy it too much because there's another big game on Monday.
"We're very happy today, but the job is far from done, we have to make sure we keep going.
"The players are very happy, they've been absolutely fantastic out there, when you win a game like this, again in the last few moments of the game and with the supporters and how they were today it's difficult to come down.
"But fortunately we're going away today, staying together for the next two days and we'll make sure everybody calms down."
Plymouth manager Ian Holloway:
"I still can't believe how we've lost, but that's life. You've got to be able to win headers in your box. "But other than that I thought we were terrific. We were calculated, we were calm, we looked a composed side, we looked like we deserved to have a few more points on the board than the team we were playing against.
"I came here not expecting to get one decision to be honest.
"You're going to have 35,000 people going absolutely ballistic, but what impressed me was that they didn't turn on their team.
"Well done to the Leeds fans and I felt their players responded to them. That's two great results they've just had so they're still in there."
Leeds: Ankergren, Richardson (Thompson 39), Michalik, Heath, Gray (Rui Marques 80), Blake (Moore 65), Kishishev, Douglas, Lewis, Healy, Cresswell.
Subs Not Used: Stack, Johnson.
Booked: Gray.
Goals: Healy 45, Michalik 87.
Plymouth: McCormick, Connolly, Timar, Seip, Sawyer, Djordjic (Sinclair 74), Norris, Nalis, Halmosi, Ebanks-Blake (Fallon 86), Hayles.
Subs Not Used: Buzsaky, Capaldi, Gosling.
Booked: Timar.
Goals: Halmosi 36.
Att: 30,034
Ref: S Mathieson (Cheshire).
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