Misbah smashed a 56-ball hundred, equalling West Indian legend Viv Richards's record made against England at Antigua in 1986, minutes after breaking the mark for the fastest fifty which he made off just 21 balls.
That set up Pakistan to declare their second innings at 293-3, setting Australia a mammoth 603-run target and on course for a 2-0 win in the series, the first over their opponents in 20 years.
Opener David Warner (24) and Michael Clarke (two) were at the crease after Chris Rogers fell for two, caught at leg slip off left-arm spinner Zulfiqar Babar.
Babar also had Glenn Maxwell leg before for four.
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Earlier Misbah, notorious for his slow batting in one-day internationals, removed all doubts about his credentials.
In all he hit 11 boundaries and five sixes off 57 balls during his two centuries in the match, a blitz which overshadowed Azhar Ali's feat of 100 not out, making this only the second occasion in Test cricket's history when two batsmen scored a century in each innings in the same match.
Misbah beat the previous record of the fastest half-century held by South Africa's Jacques Kallis scored against Zimbabwe at Cape Town in 2004.
Misbah hit two boundaries off paceman Mitchell Starc to reach his hundred, punched the air in delight and waved his bat to team-mates.
This is also the second fastest hundred in terms of time, behind Australia's Jack Gregory who reached a hundred in 70 minutes against South Africa at Johannesburg in 1921.
Misbah took 74 minutes to reach the mark.