The New South Wales fast bowler, exploiting the cracks in a wearing pitch, claimed 5 for 20 off 32 balls as New Zealand crashed to 174 all out to lose by an innings and go 2-0 down in the three-match series. Australia took the first Test in Brisbane by 186 runs and the final Test begins in Hobart, Tasmania, on Thursday.
Cook, a replacement for the injured Glenn McGrath, finished with 5 for 39 for the second innings and 7 for 75 in the match as Australia won their eighth series in a row.
The Australian captain Mark Taylor was enthusiastic about Cook's contribution to victory, which came with more than four sessions to spare, but he warned Australia would have a much greater challenge in the three-Test series against South Africa, starting in Melbourne on Boxing Day.
"The series over there earlier this year was tough enough but this will be even tougher," he said.
His counterpart Stephen Fleming was disappointed with his team's loss of the series on a tour of unbroken misery. "All the way through we have under-achieved, and that is an alarming aspect," he said. "There has got to be some soul-searching.
Resuming on the fourth day on 69 for 3, New Zealand lost their last seven wickets in 145 minutes for the addition of 105 runs.
Adam Parore extended his overnight 42 to 63, a knock that lasted almost three hours and included 10 fours but he received little assistance from his hapless team-mates.
New Zealand won toss
NEW ZEALAND - First Innings 217 (C D McMillan 54, C L Cairns 52; S K Warne 4-83).
AUSTRALIA - First Innings 461 (S R Waugh 96, M E Waugh 86, I A Healy 85, P R Reiffel 54; C L Cairns 4-95).
NEW ZEALAND - Second Innings
(Overnight: 69 for 3)
A C Parore lbw b Kasprowicz 63
* S P Fleming c Blewett b Warne 4
N J Astle lbw b Cook 19
C D McMillan lbw b Cook 23
C L Cairns b Cook 7
S B Doull c S R Waugh b Cook 17
S B O'Connor c Taylor b Cook 7
G I Allott not out 2
Extras (lb2, nb5) 7
Total (64.2 overs, 270 min) 174
Fall (cont): 3-84, 4-102, 5-137, 6-145, 7-160, 8-165, 9-174.
Bowling: Kasprowicz 16-5-43-2; Reiffel 12-4-26-0 (nb4); Warne 26-4-64- 2 (nb1); Cook 10.2-3-39-5.
Umpires: D B Hair (Aus) and G Sharp (Eng).Reuse content