Pakistan finished the second day on 97-8, 332 runs behind Australia's first innings total of 429 at the Gabba.
Hazlewood took 3-19, including two wickets in two balls, while Starc finished with figures of 3-45.
Earlier, Nathan Lyon and Jackson Bird put on 49 runs for the final Australian wicket after Peter Handscomb completed his maiden Test century.
Mohammad Amir finished with 4-97, his best bowling figures since his return to Test cricket in July following a five-year ban, while Wahab Riaz took 4-89.
Josh Hazlewood and Mitchell Starc starred as Australia took control of the day-night first Test in Brisbane.