The tourists had declared on their overnight score of 256-9 in their second innings, setting the Kiwis a testing target of 334 for victory.
But the hosts surprised Alastair Cook’s men, an unbeaten 89 from BJ Watling and woeful bowling, particularly from Graham Onions – who ended with match figures of 1-213 – saw them reach their target with just eight balls to spare.
Chris Woakes, who took 2-67, focused on the positives that England can take into the forthcoming Test series, which begins in Dunedin on Wednesday.
“We felt we had enough runs and we could bowl the team out for less than 333,” said the all-rounder.
“We back ourselves to bowl a team out on the last day and unfortunately we didn’t do that but we gave it our best shot.
“Our guys aren’t too low as we know we played some good cricket over the past four days.
“It’s good that we’ve had the chance to have a look at a few of their players, particularly their batsman.
“We have two warm-up days before the first Test so we can go away and think about our performance.”