Ricky Ponting's side claimed a 2-0 series win at Adelaide Oval on Monday as a warm-up for their heavyweight clash with South Africa, starting in Perth on December 17.
Wicketkeeper Brendon McCullum was unbeaten on 84 in a lone hand for New Zealand as they were bowled out for 203 in 74.1 overs.
Wicketkeeper Brad Haddin was named man of the match for his 169 in Australia's first innings of 535 in reply to New Zealand's 270.
Australia's Michael Clarke was man of the series after his 98 in Brisbane and 110 in Adelaide.
Returning into top form, tearaway quick Lee took 5-105, giving him nine wickets for the match for the first time in his 74-Test career.
It was also Lee's 10th five-wicket haul in an innings.
Plagued by a series of soft dismissals and a spectacular catch by Ricky Ponting, the Black Caps showed little resistance to be 5-83 at lunch on a lifeless pitch.
Australia on top in Adelaide Test
Lee struck with the second ball of the day when Aaron Redmond (19) aimed an ambitious swipe through point and was caught by Michael Clarke at 1-39.
Jesse Ryder's dismissal was also lame, caught at cover off Lee for three at 2-55.
Three runs later Ross Taylor (1) got a leading edge and was caught and bowled by Lee.
In Lee's next over, Ponting took a freakish diving catch at second slip to dismiss opener Jamie How for 28.
Left-armer Mitchell Johnson removed Daniel Flynn (9) and Peter Fulton (7).
Off-spinner Nathan Hauritz (2-32) joined the party with the important wicket of Daniel Vettori (13) and followed that with Tim Southee's demise, both caught in slips.
Tailender Iain O'Brien made a 56-minute duck, sharing a 50-run partnership for the ninth wicket with McCullum, before becoming Lee's fifth victim.
Chris Martin was bowled by Johnson (3-29) for a duck, giving the No.11 his sixth pair, a world record.
Top-ranked Australia won the two-match series 2-0 to relegate New Zealand to eighth on the ICC Test Rankings, ahead of only Bangladesh.