Azhar, playing in his 56th Test, raised his 12th Test century and third against Australia with two runs behind the wicket to fine leg.
The tourists, who trail 1-0 in the series, went to lunch at 232 for four and went through the extended first session without losing a wicket, with Azhar on 112 and Asad Shafiq not out on 48.
The pair had put on 107 runs for the fifth wicket after the loss of skipper Misbah-ul-Haq for 11 before tea on Monday's rain-hit opening day.
Shafiq, who scored a fighting 137 in Pakistan's narrow loss in the first Gabba Test, survived a review on 20 when an inside edge catch behind off Jackson Bird was found to have come off his pad.
Pakistan went to first drinks at 185 for four with Azhar seven runs short of his century. Light rain sent the players from the field midway through the opening session, before play resumed and was then stopped again just before lunch.
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