You are not permitted to download, save or email this image. Visit image gallery to purchase the image.
England's bowlers, particularly James Anderson, had done a superb job to dismiss New Zealand for 269 in 48.5 overs at a small venue with short square boundaries, where a score of at least 300 was needed to set a competitive total.
Joe Root (79 not out) then picked up from where Cook left off when the captain was dismissed by Tim Southee, while Jonathan Trott finished on 65 not out as England easily chased down the total for the loss of two wickets in 47.4 overs.
"I thought the way we bowled up front was outstanding," Cook said. "Steve Finn and James Anderson bowled really well and we gave them nothing, took some wickets and put them under pressure.
"We knew that 270 was below par on that wicket and that if we kept our heads while batting, and kept wickets in hand then, as it proved, it was quite an easy chase."
England's victory ensured the series finale at Eden Park in Auckland on Saturday would be a decider after New Zealand won the first match in Hamilton on Sunday by three wickets.
New Zealand's innings was dominated by Ross Taylor's 100, his seventh one day international century, and a brutal 74 from 36 deliveries by captain Brendon McCullum, but it was well short of a ground that consistently yields innings in excess off 300.
"I think we were probably 20 runs under par," McCullum said.
"At 270, I thought we were still a chance if we got early wickets but we weren't able to get them... (and) they played brilliantly to knock off 270 reasonably comfortably."
Taylor, who was dumped as captain by coach Mike Hesson in December and chose not to tour South Africa, had barely played any cricket since and had looked rusty in his return to the international scene.
The 28-year-old took a little time to get into his stride and also curbed his attacking instincts to anchor the innings after Anderson and Finn had put the hosts under immense pressure.
Taylor combined with Kane Williamson (33) in a 72-run partnership, then 52 runs with Grant Elliott (23) for the fourth wicket before the latter was dismissed by Finn in the first over of the batting powerplay to leave New Zealand struggling at 143-4 in the 36th over.
McCullum, however, then thrashed nine fours and four sixes in a 44-minute knock that included a 100-run partnership with Taylor, 77 of which came in 5.5 overs.
McCullum's dismissal then sparked a collapse with the final five wickets falling for 26 runs as Anderson returned to mop up the tail and finished with impressive figures of five for 34.
"I'm delighted with the way I bowled," Anderson said. "I think we bowled pretty well as a unit.
"It's a good pitch... and we knew that if we hit our areas then we would get some rewards.
"We got some early wickets and just stuck to our tasks... and kept them under 300 (which) we knew we could chase down." (Reporting by Greg Stutchbury in Wellington; Editing by John O'Brien)