Warner smashed 133 for his ninth Test century and his third in as many innings to match the indomitable Donald Bradman.
But Pakistan hit back to dismiss Australia for 303 in their first innings, for a first innings lead of 151, after they had made 454.
By the close, Pakistan had made 38-0 in their second innings with Ahmed Shehzad (22) and Azhar Ali (16) at the crease, stretching their lead to 189.
Michael Clarke failed with a 13-ball two and so did Alex Doolan (five).
It was Warner who anchored the innings, becoming seventh Australian batsmen to score three consecutive hundreds, the feat last achieved by Adam Gilchrist (2005) and Bradman (1948).
But with his third ball after lunch, Shah spun sharply to bowl Warner, who had hit 11 fours and two sixes during his 174-ball knock, but his fall saw Australia slump against spinners.
Paceman Imran Khan (1-54) had Haddin bowled off an inside edge while Babar had Marsh lbw.
Warner saw Australia lose Chris Rogers (38), Doolan and Clarke in the space of just 30 runs before he and Steven Smith (22) added 48 for the fourth wicket.
Warner drove Khan to cover boundary for his eighth four to complete his hundred off just 128 balls.
The left-hander had hit a century in each innings against South Africa at Cape Town in Australia's last Test in March this year.
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