Taylor's 119 not out and Kane Williamson's 93 did the bulk of the damage as England conceded their highest total in all one-day internationals, surpassing the 387 for five posted against them by India at Rajkot in 2008.
Chris Jordan's return of one for 97 in nine overs equalled the England record for the most expensive in an ODI innings, with former fast bowler Stephen Harmison also conceding 97 runs, but in 10 wicketless overs, against Sri Lanka at Headingley in 2006.
The most England have made batting second to win a one-day international is 306 for five, needing 305, against Pakistan at Karachi in 2000.
Tuesday's series opener at Edgbaston had seen England pile up a national record 408 for nine as they won by 210 runs.
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But Brendon McCullum didn't make the same mistake twice, the New Zealand captain opting to bat first this time after winning the toss.
McCullum took 21 off all-rounder Jordan's third over, the sixth of the innings, including two successive sixes, in the course of a typically quickfire 39.
Martin Guptill went on to complete a 51-bally fifty but was out soon afterwards when he miscued a pull off Ben Stokes to Jordan at short mid-wicket.
Taylor had a let off on seven when a diving Jason Roy at backward point failed to hold a tough chance following a fierce cut off Plunkett.