Taylor anchored the innings with a well-crafted 100, his seventh one-day century, while McCullum blasted 74 from 36 deliveries to resurrect the innings after England's bowlers had strangled New Zealand's batsmen early on.
Having won the toss and chosen to bowl, England's strike bowlers James Anderson and Steve Finn put New Zealand under immense pressure and severely restricted their scoring despite a good surface and the short square boundaries.
Such was the stranglehold that the home side made just 21 for two in the first 10 overs, Anderson taking both wickets by having BJ Watling caught in the slips for seven and debutant Hamish Rutherford caught at short mid-off for 11.
Kane Williamson and Taylor resurrected the innings, combining for a 72-run partnership before Williamson dragged a wide Chris Woakes delivery onto his leg stump for 33.
Taylor and Grant Elliott (23) put on 52 runs for the fourth wicket before the latter was dismissed by Finn in the first over of the batting powerplay to leave New Zealand struggling at 143 for four.
McCullum, however, unleashed his fireworks, thrashing nine fours and four sixes in a 44-minute knock that pushed the home side towards a respectable total.
Anderson returned to mop up the New Zealand tail and finished with impressive figures of five for 34 in 9.5 overs, while Woakes had three for 68 from 10 overs.
New Zealand lead the three-match series 1-0.
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