Joe Root 's 64 and an unbeaten 61 from Jos Buttler guided England to a total of 310 all out in Cardiff. England are sitting atop the Group A having won their opening game against Bangladesh by 8 wickets, whereas New Zealand are at No. 3 after rain washed out their clash against Australia.
Tuesday's success means England will return to the Welsh capital as Group A winners for a last four clash against the as yet unknown Group B runners-up on June 14, in an event featuring the world's leading eight one-day global teams.
Hopes of another Bangladesh victory could rest on the batting brilliance of Tamim, who has lit up the Champions Trophy with scores of 128 and 95 against England and Australia.
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There will be no let up for England in their final group match against Australia at Edgbaston on Saturday either despite the fact the hosts effectively have nothing but bragging rights to play for.
Buttler's knock which came off just 48 balls with the help of two fours and two sixes provided the just-needed impetus to England's innings to get past the 300-run mark.
"We know how well we've done and we know that if we perform to anywhere near our capability we are going to be a really tough team to beat", said England all-rounder Ben Stokes.
New Zealand and Bangladesh each have a point due to their washouts against Australia and should Steve Smith's side lose, the victor of their match on Friday in Cardiff will advance to the last four.
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After Hales' dismissal, Root stitched 54-runs partnership for the fourth wicket with Jos Buttler before the Kiwis picked up wickets at regular intervals to put brakes on England innings.
"We want to be positive, look to attack from ball one and see where it takes us".
"As a former England opener, I know just how much pressure Jason Roy will be under and all I can do is reiterate what I said before".
"I'm sure they'll be OK", Smith said. Sometimes these things heal quicker, sometimes they take longer, so we have to play it by ear.
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"We are still striving to win the game regardless of our situation with the bat because we bat so deep with such a powerful line up, but today a lot of credit goes to our bowlers". "They seem to produce limited-overs cricketers at will", the former Ireland worldwide added.
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