Only captain Brendan Taylor, with 65, offered any real resistance as Zimbabwe were bowled out for 171 in 44 overs.
It was the fourth successive heavy defeat for the tourists, after they were beaten by an innings and 301 runs in the one-off Test, and by 90 and 141 runs in the first two one-dayers.
McCullum won the toss at McLean Park and had no hesitation in batting on a good wicket.
New Zealand's total of 8-373, its highest on home soil, was set up by a another century partnership from openers Martin Guptill and Rob Nicol.
The pair put on 153, at seven runs an over, to go with their 131-run stand in game two in Whangarei, when Nicol made a century and the Black Caps ended on a similar score of 6-372.
Nicol got 61 before the stand was broken, while Guptill fell in the next delivery after making 85 from 69 balls in his third half-century of the series.
Zimbabwe was able to slow down the scoring during the middle stages of New Zealand's innings, before McCullum, batting at No.4, picked up the pace on the way to 119, his fourth ODI ton.
He had a life on 48 when Regis Chakabva spilled a regulation catch at long-off.
There was also a stutter when batting partner Andrew Ellis was run out as he tried to make it home for the run that would have got his captain to three figures.
McCullum made no mistake the next ball, driving to long off for a single.
He was dismissed on the final ball of the innings as he went for one last slog to try to improve his tally of seven fours and five sixes.
Zimbabwe completes its tour with two Twenty20 internationals, the first in Auckland on Saturday.