Martin Guptill retired hurt on 3, with a hamstring strain, then returned with New Zealand seven wickets down to help his team win with seven balls to spare.
Guptill hit a six and four fours to finish 27 not out after sharing an unbroken 51-run partnership with McCullum that carried New Zealand past England's total of 258.
Earlier, fast bowler Mitchell McClenaghan broke down with a side strain while taking his fourth wicket as New Zealand bowled out England in 49.3 overs.
McClenaghan, a 26-year-old candidate for New Zealand's Bachelor of the Year award, took 4-56 — his second four-wicket haul in a four-match international career - to help New Zealand suppress England's powerful batting lineup.
He bowled captain Alastair Cook for 4 with a full and seaming delivery, removed Stuart Broad for 1 and dangerman Jos Buttler for 21 but suffered his injury in the delivery that dismissed Steven Finn. Veteran Kyle Mills took 2-32 from his 10 overs as McClenaghan's new-ball partner to further restrict England's scoring.
England laid a strong foundation for its innings with Jonathan Trott making 68, Ian Bell 64 and Joe Root 56.
But it scored at a slow rate, relying on the fluent scorers in its middle and lower order to lift it to a competitive total. That tactic failed when, after taking such pains to set the foundation, its last six wickets fell for 38 runs.
New Zealand also suffered an early setback, losing B.J. Watling when it was on 2 and had barely recovered from that blow when Guptill limped from the field.
Kane Williamson played a giant role in restoring the New Zealand innings, making 74 from 99 balls to guide the home side to 142-4 when he was out in the 34th over.
McCullum - batting at No. 5 - then took over the leadership of the innings, reaching his half century from 48 balls with five fours and two sixes.
New Zealand's cause was still in doubt when it cheaply lost James Franklin, Nathan McCullum and Andrew Ellis to slump to 218-7. But Guptill strode back out from the pavilion and joined McCullum in the final, winning partnership.
The win was New Zealand's fifth in succession over England in one-day internationals.
"I think today was very important for us," McCullum said. "They were 180-2 at one point and to be able to show those fighting qualities and restrict them to under 260 was a fantastic effort."
England was sent in after losing the toss and eventually paid with an overly measured approach to its innings. It was only 77-1 after 20 overs and 101-2 at the midpoint of its innings. Its hopes rested with the big-hitters later in the order but they were restricted by the loss of wickets and accurate bowling.
"We got off to an okay start," Cook said. "And 260 was an okay score.
"I thought the way we bowled we defended it well but I guess 280 or 290 would have been better. When you load towards the bottom you need to go and hit the ball well and we didn't manage to get anyone to do that today."
The second match is at Napier on Wednesday.