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Pakistan lead the series 2-1 and victory would give them the six-match contest with a game to spare, while New Zealand need to win to keep the series alive.
The 19-year-old Shehzad cracked 115 off 109 deliveries in a masterful innings while none of the other Pakistan batsmen were able to seriously damage the New Zealand bowling.
Misbah-ul-Haq, the standout performer in the series so far, had a rare off day and struggled to make 25 before he hit Scott Styris to deep square leg where Jacob Oram pulled off an acrobatic catch.
Umar Akmal’s 32 before he was run out by wicketkeeper Brendon McCullum was the second highest score as New Zealand, who have lost 14 of their past 15 ODIs, produced one of their better performances in some time.
After winning the toss and opting to bowl first in overcast conditions, New Zealand made the surprise move of resting their best swing exponent Tim Southee.
But their reasoning appeared to be a preference for slower deliveries which paid dividends with medium pacers Oram and Styris taking two wickets apiece.
Styris claimed the crucial scalp of Shehzad, who hit 12 fours and three sixes in his lengthy innings.
He was striking out for another six when he was deceived by a slower ball and got under it too far, scooping a catch to James Franklin.
It was a timely performance from Shehzad who delivered on the promise he had hinted at in his previous seven international innings, which produced a total of 173 runs.
He was particularly harsh on New Zealand new ball bowler Hamish Bennett, taking all his boundaries off the speedster who returned the less than impressive figures of none for 56 off eight overs.
By the time Shehzad was dismissed Pakistan were in a healthy position of 197-4 in the 38th over but they were unable to capitalise on it over the remainder of their innings which only produced 95 more runs.
Shahid Afridi and Umar Akmal could only scrape together 39 runs in the batting power play between the 44th and 48th overs.
Ross Taylor is captaining the New Zealand side after Daniel Vettori was ruled out in the morning because of continuing troubles with a hamstring strain which flared in the fourth game in Napier on Tuesday.
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