Australia are still in command of the second Test against New Zealand despite a strong effort from Brendon McCullum's men on day two to bring themselves back into the contest.
The Baggy Greens began the day on 416-2 with David Warner unbeaten on 244, and although he was able to pass the 250 mark, he was to fall for 253 when he was dismissed by Trent Boult.
Captain Steve Smith struggled in his time at the crease before he was out for 27 to James Henry, but Adam Voges (41) and Mitchell Marsh (34) were able to do enough to guide their side over the 500-run mark.
Mark Craig took three late wickets as Australia paid the price for trying to up the run rate before Smith declared on 559-8.
The Kiwis' reply got off to the worst possible start when Martin Guptill was dismissed in the third over lbw to Mitchell Starc.
Tom Latham and Kane Williamson restored calm to the New Zealand ranks by seeing off the threat of the new ball from Mitchell Johnson and Starc.
Both players looked be finding a rhythm at the crease as they eased to a 50-run partnership from 89 deliveries and were bearing down on reaching 100 before Latham fell to the bowling of Lyon for 36.
Williamson managed to fend off a difficult spell of bowling from Johnson to record his half-century, the 17th of his Test match career.
Ross Taylor (26*) and Williamson (70*) notched the second 50-partnership of the innings just before the close, leaving New Zealand on 140-2, trailing the Aussies by 419 runs.
