They came together with Pakistan struggling at 127-6 in the 36th over, and cracked a whirlwind 71 in 38 deliveries to ensure the total at least passed the 200 mark.
But when Misbah fell for 58, his 38th half century, the last four wickets fell for just 12 runs as the innings folded with 27 balls remaining.
Afridi, who posted his 39th ODI half century, was out for 67.
New Zealand went into the match two days after completing a 4-2 series win over Sri Lanka, while Pakistan have not been tested since they lost a home series to New Zealand 3-2 before Christmas.
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Kyle Mills bowled four dot balls swinging away before bringing one back to remove Mohammad Hafeez without scoring.
He also claimed Younis Khan's wicket twice. The first time, with Younis on five, the batsman was recalled when replays showed he was caught off a no ball, but on nine he was unquestionably trapped leg before wicket.
Ahmed Shehzad and Haris Sohail went in similar fashion, flinging the bat at wide deliveries with Shehzad caught behind for 15 off Trent Boult while Sohail was snapped up by Martin Guptill at point for 23 off Corey Anderson.
But the arrival of Afridi at the start of the powerplay lifted the innings as the all-rounder cracked 67 off 29 deliveries including three sixes and nine fours.
A more circumspect Misbah, who faced 87 balls for his 58, started the tail collapse when he was caught on the boundary by Tom Latham off Grant Elliott who was the most successful New Zealand bowler with three for 26.