Hard-hitting Conway steers New Zealand to victory over South Africa
Conway's 60 off 49 balls set the home side up for a competitive 175-6 after being sent in to bat at Hamilton's Seddon Park.
The Proteas lost wickets regularly to be dismissed for 107 off 15.3 overs, with pace bowlers Ben Sears and Lockie Ferguson snaring three wickets each.
South Africa won game one in Mount Maunganui on Sunday by seven wickets.
Both sides are fielding largely second-tier lineups, choosing to rest their first-choice players in the wake of the T20 World Cup.
New Zealand lost the final of the global tournament to hosts India earlier this month, having beaten South Africa in the semi-finals.
Conway produced easily the most important innings of the game, the 34-year-old posting five fours and two sixes.
The South African-born left-hander played with controlled aggression as wickets fell around him to reach his 13th half-century in the format.
Conway was delighted to contribute after being an unused squad member throughout the World Cup.
"It has been a very quiet couple of months for me, going over to India and not featuring at the World Cup," he said.
"It's been nice to come back and play and be able to contribute for the boys and the group."
Josh Clarkson raced to 26 not out at the death while allrounder Wiaan Mulder took 2-14.
Mulder's addition was the only change to South Africa's team from game one, replacing Jordan Hermann, who was ruled out of the remainder of the series with a hamstring injury.
The tourists never recovered from 31-3 and four wickets fell for three runs late in the chase, before George Linde added some respectability by top-scoring with 33.
Game three is in Auckland on Friday.