After thrashing the hosts in the first Test by an innings and 52 runs in Wellington last week, Australia sealed the second match by seven wickets shortly after lunch on the fifth and final day at Hagley Oval.
It was Australia's seventh win in 11 games under Smith's captaincy, while the match was also the 101st and final Test for New Zealand skipper Brendon McCullum, who now heads into international retirement.
Australia were last at the summit of Test cricket in July 2014 and Smith set course for a return when he assumed the captaincy from Michael Clarke full time after last year's Ashes loss to England.
"We want to win every series we play. We want to win a lot more away from home and that was a good start for us," Smith said.

"We had a lot of patience in the way we played and ...all the guys are really confident in their skills," he added.


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