Ahmed Shehzad (55) and Younis Khan (26) were at the crease as Pakistan increased their lead to 267 with nine wickets in hand to press their advantage for a 1-0 lead in the two-Test series.
Resuming on 38-0, Pakistan lost Azhar Ali to left-arm spinner Steve O'Keefe for 30.
Pakistan had taken a 151-run lead after scoring 454 in their first innings. Australia made 303 in their first knock.
The second and final Test will be played in Abu Dhabi from October 30.