After McCullum's 51 in 19 balls had provided his side a comfortable target well under four an over, Corey Anderson stepped up with 81 to ensure the job was done.
When Anderson was dismissed New Zealand required a further 10 runs which they achieved with seven overs remaining.
Sri Lanka, electing to bat first, posted 218-9 on the back of Mahela Jayawardene's 104 in 107 balls.
It was the 18th ODI century for the 37-year-old, the fifth highest run-scorer in the history of the shortened game, who was rarely in trouble by the New Zealand attack until caught in a wicket meltdown late in the late innings.
But for McCullum that was a signal to open up as he blazed away to bring up his 50 in just 19 deliveries with six fours and three sixes.
It was the seventh fastest half century of all time, and only two behind the record held by Sri Lankan Sanath Jayasuriya, who took 17 balls to reach 50 against Pakistan in 1996.
McCullum had no sooner reached his 50 than his rollicking innings was over, beaten in the air by Sachithra Senanayake and stumped by Kumar Sangakkara to trigger a mini New Zealand collapse.
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