Australia hold a commanding 503-run lead over New Zealand after day three of the first Test at Brisbane thanks to second-innings centuries from Joe Burns and David Warner.

The Kiwis began day two in trouble on 157-5 in reply to the Baggy Greens' mammoth total of 556, with Kane Williamson and BJ Watling at the crease.

Watling was dismissed for 32 when he was caught behind by Peter Nevill off the bowling of Mitchell Johnson to leave the tourists' tail exposed.

Williamson upped the ante in his innings by finding the boundary with regularity in his partnership with Mark Craig to take the Kiwis over the 200-run mark.

The 25-year-old notched his century off 129 deliveries after the wicket of Craig for 24, but the New Zealand innings began to fall apart as Doug Bracewell and Tim Southee departed.

Williamson had a late flurry but he was the last wicket to fall for 140 when Starc had him caught behind to leave the Kiwis all out for 317.

With 239 runs already in place, Warner and Burns took the attack to the New Zealand new-ball bowlers and the openers powered their side past the 50-run mark.

Warner brought up his half-century off 44 balls, while Burns followed suit for the second time in the match by bringing his milestone up off 57 deliveries.

The duo compounded the Aussies' lead by speeding past the 100-run mark, and the duo had soon surpassed 150 runs at the crease as Burns reached his maiden Test century from 102 balls.

Warner then made his second ton of the match to put the Baggy Greens in complete control before they reached the 200-run mark.

Warner was the first wicket to fall when he was caught by Trent Boult off the bowling of Craig for 116, while Burns soon followed his opening partner back to the pavilion for 129.

Steve Smith and Mitchell Marsh were also out cheaply to leave the Aussies on 264-4 at the close in complete command of the Test.