New Zealand made 6-175 after being sent in on Tuesday on a pitch which became trickier as the evening wore on.
South Africa was bowled out for 107 in 15.3 overs as pacers Ben Sears and Lockie Ferguson took three wickets each. Batters struggled for timing on a pitch which provided variable pace and bounce and all 10 South Africa wickets fell to catches.
The tourists lost their last six wickets for 40 runs and only George Linde stood against the collapse, scoring 33 from 12 balls with three fours and three sixes.
Sears, New Zealand's travelling reserve at the recent T20 World Cup, took 3-14. Ferguson took 3-16, dismissing Linde to end the innings.
"I thought we bowled really well up to a point and then lost our way with the bat," South Africa captain Keshav Maharaj said.
New Zealand began their inning strongly with Conway scoring square of the wicket and Tom Latham using ramp shots for a six and a four over fine leg.
They were 0-43 after the powerplay and 2-81 after 10 overs, including Latham (11) picking out Ottneil Baartman at third man with a reverse sweep.
But New Zealand wasn't able to accelerate early in the second part of its innings as the dew settled and the pitch at Seddon Park became more two-paced.
Nick Kelly had 21 from 12 balls then played and missed at a ball from Wiaan Mulder and was bowled, and Mitchell Santner made 20 from 14 before being beaten by a ball from Baartman which cut back between bat and pad.
New Zealand were 4-123 after 15 and soon after lost Conway, who had held up one end for three quarters of the innings. He top-edged a pull shot to wicketkeeper Connor Esterhuizen.
Josh Clarkson cameoed with 26 from nine balls and he and Cole McConchie helped themselves to 24 runs from the last over bowled by Maharaj.
The third international will be in Auckland on Friday.
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