Mitchell Santner was in a potentially match-winning partnership with Kane Williamson when he was run out after the ball deflected on to the stumps from a dropped caught-and-bowled chance.
England captain Eoin Morgan admitted the wicket was a match-turning fluke, but he was also adamant Santner should have been given out 87 runs earlier when Jason Roy took a ground-level catch with New Zealand already in dire straits at 112 for six in reply to England's 234.
Santner progressed from two to 41 and New Zealand were 199 for six with victory in sight when Chris Woakes failed to grasp a drive from Williamson.
But the ball deflected off his fingertips into the stumps at the non-striker's end where Santner was out of his crease.
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"You earn a little bit of luck along the way," Morgan said Sunday as the teams prepared to move to Dunedin for game four on Wednesday.
But Morgan was certain Santner had been legitimately caught when he clipped a Moeen Ali ball to Roy at midwicket in an incident similar to a denied catch in a Twenty20 match against Australia in Hobart last month.
- 'Don't celebrate' -
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"I think it was the exact same," Morgan said. "I had a worse view of this one, but on the TV it's not going to look out, from front on. He (Roy) said he had his fingers under it and I believe him."
"After the decision in Hobart we were told 'if you can, don't celebrate or throw the ball away, throw the ball in until it's called dead'. We celebrated in Hobart, and they ran one.
"We were told if he threw the ball up and it went over the rope it would be five overthrows if it was given not out.
"That went around the team and everyone knows it now, regardless of whether it's a tight catch, which is hard to do."
"It potentially could have (cost us) if we didn't get that run out, but there's no other solution to it," he said.
"If the umpire's unsure he has every right to go upstairs and on TV it just doesn't look out.