England vs New Zealand: England beat NZ by 8 wickets in 2nd ODI
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New Zealand's former captain Ross Taylor made 100 and present captain Brendon McCullum 74 as the home side was dismissed for 269 after being sent in to bat at McLean Park.
England skipper Cook scored with 78, Root made an unbeaten 79 and Jonathan Trott reached 65 not out as the tourists chased down the total with 14 balls to spare.
The deciding match is in Auckland on Saturday.
Cook, who was out for 4 in the opening match of the series last Friday, paced the first half of the innings in partnerships of 89 with Ian Bell (44) for the first wicket and 60 with Jonathan Trott for the second. He reached his half century from 68 balls and was out in the 32nd over when England were 149-2.
Trott and youngster Joe Root then saw England comfortably home. Root made his third half century in only his sixth one-day international and smashed his 79 from 56 balls. Trott came to the wicket exactly 12 overs before Root but followed him to a half century -- he reached the mark from 63 balls with one boundary while Root did so from 39 balls with four fours and a six.
Trott was at the wicket when Root hit the winning single off Kyle Mills in the 48th over.
"It's been a bizarre series, really," McCullum said.
"They win one, we win one, they win one, we win one. Hopefully, it will continue like that this weekend and we'll take the series 2-1."
While the England batting was outstanding, the win was largely set up in the opening overs of the match by the new-ball pair of James Anderson and Steven Finn. They stifled New Zealand's scoring and claimed the early wickets of openers B J Watling for 7 and Hamish Rutherford, on debut, for 11. Anderson, bowling superbly into a strong easterly wind gusting off the Pacific Ocean, finished with 5-34 from his 10 overs while Finn, experimenting with a short run, took 1-33. Chris Woakes chipped in with 3-68.
"I thought the way we bowled up front was outstanding," Cook said. "Steven Finn and James Anderson really bowled well.
"We gave them nothing to get going, took some wickets and put them under pressure. It was really only a fantastic knock by Brendon McCullum that got them up to a decent score."
After 10 overs New Zealand was 21-2, after 20it was 59-2 and at the midpoint of the innings 89-2 while England was 106-1 after 25 overs.
"The England bowlers put us under a lot of pressure early on today and kept us at bay," McCullum said. "Obviously with their batting as well they played brilliantly to be able to knock off 270 reasonably comfortably."
McCullum boosted New Zealand toward a competitive total, reaching his half century from only 26 balls with a six off Stuart Broad. When Broad claimed his wicket in the 47th over, McCullum had hit 74 runs from 36 balls with nine boundaries and four sixes.
Taylor scratched for runs at first, battling ongoing problems with timing and judgment, but he settled, then blossomed when McCullum relieved the pressure on the New Zealand middle order. The former captain, fired and replaced by McCullum late last year, provided the perfect foil for his new captain in a partnership which provided exactly 100 runs from nine overs.
Cook wasn't able to restrain the New Zealand pair but he rotated his bowling attack expertly and after slowing the scoring at the top of the innings, he reintroduced Anderson and Finn and closed down the scoring at the end. New Zealand was 243-5 when McCullum was out but lost its last six wickets for 26 runs.