New Zealand, who were all out for 246 in 45.3 overs, managed to dismiss Australia for 191 in 43.4 overs to give them a 2-1 series win that helped them retain the Chappell-Hadlee Trophy, which is played for between the two countries in one-dayers.
The 34-year-old McCullum is retiring from all international cricket at the conclusion of the two-test series against the same opponents.
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The win, however, was marred by a surreal period of play when the crowd appeared to influence a decision on the field. All-rounder Mitchell Marsh, who took 3-34 in New Zealand's innings, appeared well-set on 41 with his side 164-5 in the 34th over before he hit a delivery back to bowler Matt Henry. Henry half-heartedly appealed for a caught and bowled but it was turned down.
The giant television screen at the ground then showed a replay that created a huge uproar from the crowd who thought it had cannoned into Marsh's boot before popping back to the bowler.
Umpires Ian Gould and Derek Walker then asked third umpire Sundaram Ravi for a review after they also saw the replay and heard the crowd reaction.
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Slow-motion cameras showed the ball had not hit the ground before Henry took the catch and Ravi told Gould to give the Australian out, which caused an angry outburst from Marsh and his batting partner Matthew Wade.
The tall-right hander, who was man of the match in the second game in Wellington on Saturday with 69 not out and 2-30 in Australia's four-wicket victory, had put his side back in control of the outcome. Marsh and George Bailey (33) combined for a 59-run stand after the visitors had slumped to 94-4 in the 19th over.
Once Marsh was dismissed, however, the Australians fell apart with Corey Anderson grabbing two victims as their last five wickets fell for 27 runs. Earlier, McCullum and Martin Guptill had again got New Zealand off to a rollicking start, racing to 84 in 9.3 overs before the captain became the first of Marsh's three wickets when he was dismissed for 47.
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New Zealand's batsmen, again all got starts, but for the third time in the series were dismissed just when they needed to push on. Guptill scored 59 and Grant Elliott added 50 for the hosts, who lost their last five wickets for nine runs.
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