The Pakistan captain reached his century in 56 balls at Sheikh Zayed Stadium, matching the previous best effort of West Indian great Sir Vivian Richards, who achieved the feat against England in 1986.
Earlier, Misbah reached his 50 off 21 deliveries with the last ball before lunch, turning Mitchell Starc to the mid-wicket boundary for three runs, eclipsing the previous record of fastest 50 from 24 balls by South Africa's Jacques Kallis against Zimbabwe at Newlands in 2005.
It was only the second time in test cricket that two teammates made centuries in both innings of a match. The previous occasion was in Wellington in 1974 when Australian brothers Ian (145, 121) and Greg Chappell (247 not out, 133) both did so.
Misbah got to his fifty in just 23 minutes, and took a further 34 balls and 51 minutes to reach his hundred. In all, Misbah slammed five sixes and 11 fours.
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Australia will rue the fact that Peter Siddle dropped a catch off the second ball Misbah faced in his innings from Steven Smith when on four.
Australia will need to produce a history-making second innings if it is to win the match and level the series. A draw or a win would give Pakistan a rare series win over Australia, its first since 1994.