Australia scored an imposing total of 378-5 after being sent into bat. New Zealand captain Kane Williamson later scored 81 and Jimmy Neesham added 74 but New Zealand was bowled out for 262 in the 48th over.
Some pre-toss rain induced Williamson to bowl first despite the fact that the small Manuka Oval had been kind to teams batting first in the past five ODIs at the ground - 348, 411, 372, 267 and 329 runs had been put on the board.
Australia captain Steve Smith, who scored 164 runs to lead Australia to a 68-run win in Sydney on Sunday in the opening match, scored 72 on Tuesday.
New Zealand bowlers Matt Henry, Trent Boult, Colin de Grandhomme and Neesham conceded more than seven runs per over.
Warner became the first Australian to score six one-day centuries in a calendar year and sits third on the all-time list in a season behind Sachin Tendulkar (nine) and Sourav Ganguly (seven).
Warner was out after a diving catch by Williamson at cover in the 37th over with the home side well in control at 213-2. Smith's innings included 14 fours and one six.
Despite Warner's prolific output, he said he came into the match upset at having not posted a big score.
"I think there was a bit of frustration there," he said after making his 10th career one-day century. "When you are hitting them well in the nets, and you get some unlucky dismissals and out to wild shots trying to hit the ball, it can become frustrating."
Warner has scored 1,220 runs from 22 ODI innings at an average of 58.66 this year.
The third match is scheduled for Melbourne on Friday.