Joe Root scored a century before England's bowlers knocked over New Zealand for 259 in the final session of day three in Wellington, clinching a series on New Zealand soil for the first time since 2008.

As with their eight-wicket loss in Christchurch, New Zealand were outplayed for long periods, although Tom Blundell showed some late resistance with a century as he fought bravely in the unlikely pursuit of a winning target of 583.

The wicketkeeper was dismissed for 115 soon after tea, caught brilliantly by slip Ben Duckett off spinner Shoaib Bashir to spark a tail-order collapse.

Nathan Smith (42) and Matt Henry (4) both fell to Ben Stokes (3-5) before the England skipper removed Tim Southee (8), caught in the deep in the game's final act.

Stokes said it was "amazing" to win the series playing the sort of front-foot style they have made a trademark under his leadership.

He praised Harry Brook's "bravery" in his thrilling first-day knock of 123 which swung the momentum after New Zealand's seamers claimed four early scalps.

"That wicket is what we call a snakepit, especially on day one, it was doing plenty," Stokes said at the Basin Reserve.

"For Brooky to have the bravery and the backing of his own ability -- but to also have the skill to go out and play like that -- was just absolutely phenomenal.

"Brooky thought that putting the pressure back on the New Zealand bowlers was exactly what was needed, knocking them off their length."

With England sensing a quick victory, Root set the tone on day three by posting his 36th century before being dismissed for 106, prompting a declaration half an hour after the resumption with England 427-6.

New Zealand, who have looked nothing like the side that recently stunned India 3-0 away, limped to 59-4 at lunch in response.

Their innings gained some respectability in the middle session through the efforts of Blundell, Smith and Daryl Mitchell (32).

Despite his team's plight Blundell was prepared to play shots, compiling 13 fours and five sixes as he achieved a fifth century to end a lean run of form.

Stokes, whose side was beaten in Pakistan last time out, said he was always confident they wouldn't need a fourth day to complete a rampant victory.

"Look, 580 is a lot of runs wherever you are, there's always going to be pressure on New Zealand to chase that down, particularly on that wicket," he said.

Stokes, who saw seamer Gus Atkinson take a hat-trick on Saturday, added: "The bowling performances throughout the first two games have just been exceptional."

The blustery conditions on Sunday didn't bother England's new-ball attack, with veteran Chris Woakes (2-20) thriving into a strong wind.

He clean-bowled out-of-form opener Devon Conway without scoring before claiming the prized scalp of Kane Williamson for four, caught behind.

Brydon Carse (2-53) dismissed Tom Latham for 24 with a sharp, one-handed caught and bowled, before enticing Rachin Ravindra (6) into a loose shot which was snicked.

Before that, Stokes was 49 not out when he made his declaration, having put on 100 for the sixth wicket with Root off just 13.2 overs.

They added 49 to their overnight score, allowing time for Root to complete a classy ton.

Root, who resumed on 73, reached three figures with a spectacular reverse lap shot which flew over Blundell's head off paceman Will O'Rourke.

New Zealand captain Latham said two heavy losses left his team "obviously hurting" but they would aim to salvage some pride in the third and final Test starting in Hamilton on Saturday.

"We came here with hopes today of putting up some good partnerships but losing three or four (wickets) early on put us on the back foot," he said.

"England put us under pressure and when they've done that, they've managed to put the foot on the throat. 

"They're playing some great cricket at the moment."