Pakistan finished the day on 70-2 in their second innings, 419 runs behind their hosts with two days remaining.
Australia captain Steve Smith opted not to enforce the follow-on after his bowlers dismissed Pakistan for 142.
Smith hit a quickfire 63 from 70 balls as the home side declared on 202-5 to extend the lead to 489 runs.
He was helped in the quest for quick runs by Usman Khawaja, who top scored with 74 from 109 deliveries.
Pakistan lost seven wickets for just 24 runs under the Brisbane lights on day two, but coped better with the conditions when asked to bat again.
Opener Azhar Ali batted through the final two-and-a-half-hour session to reach the close undefeated on 41 from 104 balls.
But Australia remain on course for victory with a day to spare at the Gabba after Starc dismissed Sami Aslam in the 12th over, then Lyon took the wicket of Babar Azam seven overs before the close.
Nathan Lyon and Mitchell Starc made late breakthroughs to leave Australia firmly in control after the third day of the first Test against Pakistan.