New Zealand said their comprehensive innings victory over England was among their very best after Neil Wagner's five-wicket burst sealed the first Test in Mount Maunganui on Monday.

The tireless left-armer took the last two England wickets in successive balls for a five-wicket haul and to complete the rout by an innings and 65 runs late on the final day.

While England captain Joe Root lamented a disappointing batting effort, and the lack of a bowler with Wagner's application, New Zealand skipper Kane Williamson celebrated his side's match-defining innings of 615 for nine declared.

"To lose the toss and be 350 behind in the first innings it required something special," Williamson said.

"It's certainly right up there in terms of a tough, grinding Test victory."

BJ Watling's 205 and Mitchell Santner's 126 laid the platform for New Zealand's colossal 262-run first-innings lead.

England, resuming the final day at 55 for three and needing to bat through to stumps to save the Test, progressed patiently to 121 for four before New Zealand removed the last six wickets for 76 runs.

Wagner finished with five for 44 while Santner took three for 53.

"We saw the wicket deteriorate and knew if you could hit the wicket hard you would get some variable bounce. That allowed us to make the breakthroughs," Williamson said, admitting that he had concerns about how the match would finish.

"England have experience and some world-class players who've batted out draws before. If they were better than us today they were going to be able to save it. It did come down to the wire."

Archer 'could unleash more'

Root said England did not help themselves with the way they batted.

"Clearly some of the shots today were not good. Everyone's very aware of that. You can't fault effort but I put my hand up as well, that ball was treated with far too much respect."

Root said the England bowlers also needed to learn from the effort Wagner put in.

"He runs in all day and makes sure every ball means something," Root said, adding there were times England quick Jofra Archer could "unleash a little bit more".

"You have to give credit to guys like Neil Wagner who makes sure he gets the most out of himself and does a really good job for his team."

The lop-sided win put New Zealand in an unbeatable position in the two-Test series and extended their home streak to a remarkable seven series without defeat.

However, their celebrations were tempered by injury, with Trent Boult bowling just one over in the morning before leaving the field with a rib problem and taking no further part.

Williamson, who had been troubled by a hip injury in the lead-up to the Test, left the field a few overs before the end clutching his side.

The captain was confident he would be fit for the second Test while Boult was to undergo further medical examinations on Tuesday.

The second and final Test starts in Hamilton on Friday.