With Smith smacking 53 off 46 balls, Australia polished off the 131 runs they needed on the last day to reach their 201 target just after lunch in what was New Zealand captain Brendon McCullum's final Test.
The match had no sooner finished than Smith was charged over Tuesday's profanity-laced confrontation with the umpires that earlier saw fast bowler Josh Hazlewood fined 15 percent of his match fee.
The victory confirmed Australia's superiority after they won the first Test by an innings and 52 runs, and allowed them to overtake India as the world's top Test side.
"It's always special when you get to number one in the world. That's our goal as a team to be number one in the world in every format of the game," Smith said.
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"I don't think we're not nice guys. We play a good hard, aggressive brand of cricket," Smith said.
"For us it's about knowing where that line is and myself and Josh Hazlewood have crossed that line in this Test match and that's not what we're about.
"Hopefully we can learn from that and continue to develop as a team and get better."
- 'Not the ideal' exit -
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For New Zealand the drubbing by their arch-rivals put a cloud on the much-loved McCullum's farewell, as their captain took his final bow on the world stage after 101 Tests.
The brittle animosity throughout the series, which came
to a head on Tuesday, was put aside the moment Voges hit the winning runs with a four.
Smith immediately searched out McCullum to shake his hand and congratulate him on his career, which included a record 54-ball century in the first innings.
"The way he played in the first innings to score the fastest ever Test 100 is testament to the guy's character," Smith said.
"They were under the pump and he came out and took the game on and got them into a pretty good position."
After resuming Wednesday at 70 for 1, with David Warner (22) out late the previous evening, Australia took 34 overs to score the remaining 131 runs required.
Khawaja took his overnight 19 to 45 before giving Tim Southee his first wicket of the Test after 29 overs.
Southee had bottled up Khawaja for eight consecutive deliveries before getting an edge with a ball angling away outside off stump which went to McCullum at first slip.
Man-of-the-match Joe Burns, having laid the foundations for victory with his 170 in the first innings, scored his fourth Test 50 before being bowled by Trent Boult for 65 just before lunch.
This was the last Test before cricket's attention turns to the World Twenty20 championship in India next month.