Haddin hit five sixes and seven fours in his 110 off 121 balls and shared a stand of 151 with Ricky Ponting (69).
He was eventually stumped off Daniel Vettori but Cameron White and Adam Voges saw Australia home at 248-4.
Earlier, Ryan Harris and Mitchell Johnson took three wickets each as New Zealand were bowled out for 245.
Having been put in, the home side stuttered to 55-3 before Ross Taylor, passed fit to play after a leg injury, led a revival with an aggressive innings of 62 off 66 balls.
He added 71 for the fourth wicket with Neil Broom (24) but the pair departed in quick succession, with Taylor clearly angry with himself after pulling a short ball from Shane Watson straight to the boundary fielder at square leg.
Scott Styris (41) and Gareth Hopkins (45) pushed the total past 200 with a stand of 67 but the Kiwis failed to use up their full allocation and were all out in the 47th over when Shane Bond was caught behind off Johnson, who finished with 3-41.
New Zealand had a chance to remove Haddin at the start of Australia’s reply but fast bowler Bond was unable to hang onto a difficult caught and bowled chance in the seventh over.
They managed a breakthrough when Hopkins ran out Watson for 15, only for Haddin and Ponting to put Australia firmly on top with some magnificent strokeplay, going along at six an over during the 25 overs they were together.
Ponting was eventually caught at mid-wicket off Michael Mason but Haddin progressed to his hundred after an anxious moment on 83 when it looked like he had holed out in the deep, only for Tim Southee to drop the chance when his elbows hit the ground.
Southee picked himself up to dismiss Mike Hussey for nine but the game was firmly in Australia’s grasp when Haddin was lured out of his crease by Vettori and White helped himself to an unbeaten 25 before Voges hit the winning boundary to finish on 13 not out.
“It was a total that was 40 or 50 runs short and we couldn’t put any pressure on Australia because of it,” Kiwi skipper Vettori lamented.
“I suppose it’s just taking ownership of your innings and realising that 20s and 30s and even 50s and 60s aren’t good enough against Australia. You need guys to kick on. You need those big partnerships and you can’t consistently lose wickets.
“Then at times we did a really good job with the ball and at times we were poor.”
Meanwhile Ponting was delighted with his team’s response with the bat, after they failed to fully maximise promising positions in the two previous matches.
“We’ve been looking for this performance the entire series and we’ve played our best game to date. The momentum, if there is any to be taken out of this game, is obviously with us,” he said.
“It’s what we’ve been asking our top order to deliver. I said to the boys that if someone in our top order gets 80 plus or 100 we’re going to get well over 300 every time we bat with the nature of these grounds over here.
“Luckily we were chasing 240. Our bowlers did a great job there taking wickets consistently through the New Zealand batting innings.
“It was a more commanding performance and Brad obviously played a massive role in us winning.”
The fourth match of the series takes place in Auckland tomorrow and Australia’s squad will be reinforced by Tasmania captain George Bailey, a replacement for Michael Clarke, who has flown home for personal reasons.
“I’m ready to play. We’ve hit so many balls over the summer, I feel like I’m in pretty good form at the moment, so it’s just a matter of ticking over,” Bailey commented.
