The tourists went to lunch on 511 for eight in their second innings before declaring.
Australia added 178 off 39 overs in the extended morning session, with Nathan Hauritz unbeaten on 41 and Ryan Harris on 18 after adding an unbroken 58 for the ninth wicket.
New Zealand's spinners suffered today, with captain Daniel Vettori ending the session with two for 140 off 48 while Jeetan Patel conceded 79 off 12 overs for overall figures of one for 141 off 39.
Paceman Brent Arnel was the most successful, with three for 77 off 26.
Australia continued their batting dominance early in the day, adding 86 off 19 overs before the first drinks break for the loss of Michael Clarke's wicket.
Clarke and North each brought up their half-centuries off 79 deliveries and added 142 for the fifth wicket.
Arnel finally broke the partnership when he angled a delivery in to Clarke, on 63, and umpire Aleem Dar obliged.
Clarke challenged the call under the umpire decision review system but replays confirmed it was the correct decision.
North and Brad Haddin then wiped any thoughts of a New Zealand run chase of under 400 when they plundered 54 off 49 balls for the sixth wicket.
North, who hit 70 of his runs in boundaries, reached 90 before he tried to sweep Vettori and was snaffled down the leg side by gloveman Brendon McCullum.
It was Vettori's first wicket of the innings in his 40th over. But his tally quickly doubled as he had Mitchell Johnson caught at long-on, first ball, but Nathan Hauritz survived the hat-trick ball.
Haddin whacked four fours and three sixes in his 48 off 40 balls before he tried another big shot against Patel and was bowled.
