All three, Bell (64), Trott (68) and Root (56), provided a platform from which England could attack in the final overs but the visitors failed to truly capitalise on the small ground hosting the opener of the three-match series.
New Zealand's bowlers had kept the England batsmen in check early in the innings restricting them to 77 for one by the 20th over, before the trio began to milk singles at will and looked well placed to set up a score close to 300.
Trott and Root, however, did not take full advantage of the batting powerplay between the 36th and 40th over when they managed just 27 runs for the loss of the former when he was bowled by Kyle Mills.
Eion Morgan (one) fell immediately after the powerplay ended while the dangerous Jos Buttler (21) failed to push on after making a start as Mills, James Franklin and Mitchell McClenaghan ran through England's tail.
The visitors will need to bowl and field as well as they can if they are to defend a total at least 30 runs short of what is considered par for the ground.
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