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McCullum finished on 69 while Guptill, who retired hurt on three after he strained his left hamstring only to return when New Zealand were 218 for seven, was on 27 as the hosts scored 259-7 in 48.5 overs, having bowled England out for 258.
The 31-year-old McCullum had needed to provide the game-winning innings after he ran out Kane Williamson earlier when New Zealand appeared well placed for victory at 142-3 in the 34th over.
The dismissal came with Williamson on 74 and McCullum starting to look settled as the batting power play approached.
Williamson, who had been the most assured of New Zealand's batsmen, guiding the ball around the ground with ease, was run out when McCullum called for a single, changed his mind and left his partner short of his ground at the non-striker's end.
His departure produced a tighter-than-expected finish as New Zealand wickets fell regularly before McCullum seized the initiative and Guptill returned to flail away and give the hosts a 1-0 series lead.
England were dismissed for 258 in the final over of their innings after Ian Bell (64), Jonathan Trott (68) and Joe Root (56), provided a platform from which England could attack in the final overs but the visitors failed to capitalise on the small ground hosting the opener of the three-match series.
Trott's dismissal at 184-3 in the 39th over actually sparked a dramatic loss of momentum as the visitors went on to lose their final six wickets for 38 runs in six overs.
Mitchell McClenaghan finished with figures of four for 56 from 9.4 overs but he picked up a side strain that his captain believes could rule him out for the remainder of the series.