Josh Hazlewood starred with the ball and Shaun Marsh did the heavy lifting with the bat as Australia clinched a series victory over New Zealand by winning the first day-night Test inside three days.

Already sure of at least a drawn series, hosts Australia held a 22-run lead after the first innings and had reduced New Zealand to 116-5 in their second innings by the close of day two.

The tourists were all out for 208, giving Australia a target of 187 to win in Adelaide, as the bowlers continued to dictate proceedings with the pink ball, Hazlewood taking a further three wickets to finish the second innings with Test-best figures of 6-70.

Three quick New Zealand wickets set up a tense chase but Marsh's 49 and strong partnerships with Adam Voges (28) and younger sibling Mitchell (28) - the brothers batting together for the first time in Tests - gave Australia command.

After both Marsh brothers and Peter Nevill (10) departed it was left to Peter Siddle (9 not out) to hit the winning runs and deal New Zealand their first Test series loss since June 2013.

Hazlewood set up the win with a fine display, striking in the second over of day three to remove BJ Watling (7) and then dismissing Mark Craig (15) caught behind to take his fifth wicket of the innings. 

Doug Bracewell helped keep the scoreboard ticking over for New Zealand with an unbeaten 27 but Test debutant Mitchell Santner (45) and Tim Southee (13) fell to Nathan Lyon (1-36) and Mitchell Marsh (3-59) respectively. 

Hazlewood secured career-best figures by cleaning up Trent Boult (5), but the left-armer had Australia three down less than 14 overs into their chase.

Boult (5-60) trapped Joe Burns (11) lbw and dismissed Australia captain Steve Smith (14) in the same manner on review after David Warner (35) had edged Bracewell (1-37) to Southee at second slip.

However, Voges and Shaun Marsh tilted the momentum back in Australia's favour by taking the hosts to three figures before the final session.

After Voges fell to Boult, the Marsh siblings picked up the pace in an attempt to take the game away from the Black Caps, Mitchell's 29-ball cameo featuring two fours and a six, which he followed by skying Santner to Kane Williamson.

A tentative stroke saw Shaun Marsh's gutsy spell at the crease ended by Boult and nerves were jangling as Nevill, Australia's final recognised batsman, inside-edged the same bowler to Watling, who took a stunning catch to his left.

The tense mood in the Adelaide Oval was hardly sated as Mitchell Starc - nursing a fractured foot - limped out to join Siddle, but the 31-year-old held his nerve after finding fielders and smashing the stumps with a glorious straight drive that would have won the match to finally squeeze the victorious runs through point.