Shehzad was unbeaten on 128 while Younis Khan was on 67 not out as the two added 160 runs for the unbroken second wicket stand to help Pakistan reach 231-1 at tea, leaving Australia on the back foot.
Shehzad, 22, drove paceman Peter Siddle for his eighth four towards long-on to reach his second Test hundred as Pakistan increased their lead to 382 with four sessions left in the game to put themselves in a strong position to take a 1-0 lead in the two-match series.
Pakistan, 116-1 at lunch, cut loose in the second session as they looked for quick runs to set a target for Australia, with Shehzad and Younis punishing a hapless Australian attack on a flat pitch.
Shehzad smashed a four and a six off Steve O'Keefe and then hit Mitchell Marsh twice to the ropes to enter the 90s.
After reaching his hundred, Shehzad smashed two fours and a six off Siddle to take the lead past 370.
In all, he has hit ten fours and four sixes during his 228-ball knock.
But O'Keefe got his reward when he induced an edge off Ali straight into the hands of Haddin with the score at 71. Ali made 30.
Younis hit a six off Lyon and then drove Mitchell Johnson to cover bounadry to complete his 29th half-century in Tests, following his superb run of form after his first innings 106.
The second and final Test will start in Abu Dhabi from October 30.
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