Hazlewood took the first wicket with the pink ball in a test match when he trapped Martin Guptill lbw in the fourth over at the Adelaide Oval, and returned to take the first test wicket in a night session when he removed B.J. Watling (29) in the third over after the dinner interval.
He also snared the last wicket to return 3-66, as the New Zealanders were bowled out in 65.1 overs, leaving Australia 22 overs to bat under lights on day one of the third test.
Starc returned 3-24 before leaving the field with an ankle injury and heading to a hospital for scans, leaving Australia team masseur Grant Baldwin to fill in as a substitute fielder.
New Zealand started positively after Brendon McCullum won the toss, reaching 80-2 in the first session after play started at 2 p.m. local time. But Australia dominated the evening session, taking five wickets — including three for four runs within 11 balls, all caught behind by Peter Nevill — to remove Tom Latham (50), Ross Taylor (21), McCullum (4), Mitch Santer, who scored 31 from 46 balls in his first test innings, and Mark Craig (11).
The crowd swelled to 44,405 ahead of the night session, in time to see Australia wrap up the last three New Zealand wickets within eight overs of the dinner break.
Both wickets in the first session went to lbw decisions, with Hazlewood trapping Guptill (1) in front with the total at 7, and Starc hitting Kane Williamson (22) on the foot with an in-swinging yorker to end a 52-run second-wicket stand, after Nathan Lyon (2-42) and Peter Siddle (2-54) dried up the run-rate in the second hour.
Latham raised his half century with a cut boundary against Lyon in the over before tea but didn't add to his total after the interval, when a ceremony to mark the first anniversary of former Australia batsman Phillip Hughes' death was held at 4:08 p.m.
Latham got a top-edge to an attempted cut off Lyon to end the 35-run third-wicket stand with Taylor, who got an inside edge to Siddle and was also caught behind.
Skipper McCullum compounded the pressure when he slashed at Starc and was also caught by the wicketkeeper.
Santner and Watling steadied the innings, adding 44 runs for the sixth wicket before Starc bowled Santner.
Lyon picked up his second wicket when he bowled Craig as the lights were due to come on.
Hazlewood took two wickets in the last session and Siddle, recalled to the lineup to replace retired paceman Mitchell Johnson, collected his 200th career test wicket when he had Doug Bracewell (11) caught by Joe Burns.
The experimental pink ball withstood the first two sessions and didn't really produce any exceptional difference to the regulation red balls. For the record: Starc bowled the first delivery with the pink ball in a test match, and Guptill faced it.
Australia leads the three-test series 1-0 after a 208-run win in Brisbane and a high-scoring draw in Perth.
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