New Zealand captain Kane Williamson made the unusual decision to bat first after winning the toss and the Black Caps managed only 147-8 in their 20 overs, stalled by tight bowling from Haris Rauf and Mohammad Wasim.
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The New Zealanders then had to bowl as spring temperatures dropped to single figures and the outfield at Hagley Oval became damp and dewy. The bowlers could do little to arrest Babar and Shadab as the ball became wet and slippery.
New Zealand was 70-1 after 10 overs with Devon Conway and Kane Williamson at the crease. Conway made 36 from 35 balls and Williamson 31 from 30 in an innings which promised a more robust total. But the pair were out within two overs of each other as New Zealand slumped to 137-6.
Mark Chapman produced a defiant inning for the home side with 32 from 16, including three fours and two sixes. But he was out at 142 as New Zealand lost five wickets for 33 runs in the last five overs.
New Zealand might have had some hope when top-ranked T20 batter Mohammad Rizwan fell lbw to Tim Southee for 4 in the fifth over, leaving Pakistan on 36-1. But the partnership between Babar and Shadab, which came as the cold settled in, shut New Zealand out of the game.
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Shadab batted higher in the order than usual and struck two fours and two sixes in a 22-ball inning of 34.
Babar reached his half-century from 33 balls and was able to control Pakistan's run chase, leading his team to victory with 10 balls remaining. He struck the ball with superb power and placement to tally 11 boundaries.
New Zealand had a faint hope still as Pakistan needed 24 runs from the last 18 balls. But Babar struck two fours and Haider Ali hit a four and a six in the 18th over, bowled by Blair Tickner, to make the finish to the run chase a cakewalk.
Pakistan won the opening match of the tri-series by 21 runs over Bangladesh. New Zealand will play Bangladesh on Sunday. The series is the last buildup for the teams ahead of the T20 World Cup which begins in Australia in Oct.
