South Africa won the toss and elected to field first, with New Zealand posting 175 for six in their 20 overs.
The tourists were always struggling in their reply and were bowled out for 107 to slip to a heavy defeat on a sticky wicket where the ball did not come on to the bat as they might have expected.
New Zealand’s innings was powered by Conway at the top of the order, with Josh Clarkson providing an unbeaten 26 from just nine deliveries to give the score a boost in the closing overs.
Teenage seamer Nqobani Mokoena was economical with 0-22 in his four overs, while all-rounder Wiaan Mulder took 2-14 in two overs.
"It was trying to build a partnership, trying to calm myself down," Conway said. "Facing a bowler from around the wicket was something new for me. It has been pretty quite a few months for me, going to India and not featuring in the World Cup.
"I have played with some of the South Africa guys growing up and if they speak Afrikaans I can understand."
South Africa never got going in reply, losing wickets at regular intervals as George Linde top-scored with 33 from 12 deliveries.
Lockie Ferguson took 3-16 in 3.3 overs and Ben Sears 3-14 in his three overs as the pick of the home bowlers.
"I think we bowled really well but lost our way with the bat," South Africa captain Keshav Maharaj said. "There was dew but the pitch got worse to bat on.
"As a seam-bowling unit, the guys have done really well. And there was some salvaging from George with the bat, so there were some positives. It's good to have fans whereever we go."
The series is being played in conjunction with the women’s national teams of both countries and, after
South Africa lost the opener on Sunday, they bounced back to beat New Zealand by 18 runs to level that series at 1-1 as well.
