Lyon took two wickets on Monday to finish with 4-91 for Australia, who can take the top test ranking from India with a series victory.
The second game starts in Christchurch on Feb. 20.
Mark Craig, who top scored in New Zealand's first innings with 41 not out, was left 33 not out when Trent Boult was bowled by Mitchell Marsh for 12 to wrap up their second innings for 327.
New Zealand were dismissed for 183 in their first innings and faced a deficit of 379 runs after Adam Voges' second test double century drove Australia to a mammoth 562.
The visitors captured the last six wickets on Monday without the experienced Peter Siddle, who bowled just eight overs on Sunday before succumbing to a back spasm.
Marsh, Lyon and Jackson Bird all grabbed wickets before lunch to set up the victory push in the middle session.
Hazlewood trapped Doug Bracewell in front for 14 just three deliveries after they returned from the break.
While Tim Southee provided some typical rearguard fireworks with 48 from 23 balls, the result was only a matter of time with him in the mood to swing for the fences.
Southee holed out at long on trying to hit a fourth six off Lyon before Boult was bowled by Marsh just under an hour into the final session.
The only bright spot for New Zealand was debutant Henry Nicholls scoring his first test half century before he was bowled by Bird for 59.
Hazlewood's ability to get the older ball to reverse swing should be of concern for New Zealand, whose top-four batsmen made solid starts but failed to push on in what were considered good batting conditions.
The hosts had resumed on Thursday on 178-4, with Nicholls on 31. Anderson joined him after captain Brendon McCullum was trapped lbw in the final over of the third day.
Australia, however, simply chipped away and waited for the batsmen to make errors with Anderson trapped in front by Marsh for a 22-ball duck before wicketkeeper BJ Watling got an inside edge to a Lyon delivery and played on for 10.
Nicholls also played on a delivery from Bird, which gave the tall pace bowler his first wicket of the match.
(Editing by Peter Rutherford)
Share
