New Zealand will play their first match of the tournament when they meet the Proteas at the same venue on Wednesday.
Zimbabwe were restricted to 141-6 after being sent in, with captain Sikandar Raza top-scoring with 54*.
Both teams showed multiple changes following a two-match Test series in Bulawayo, which South Africa won comfortably.
Opening bowler Lungi Ngidi took a wicket and conceded only seven runs in a three-over opening spell.
Left-arm spinner George Linde took 3-10, including two wickets for four runs in the last over.
The Proteas lost three wickets in the six-over powerplay against aggressive left-arm fast bowler Richard Ngarava and seamer Trevor Gwandu.
But new cap Rubin Hermann (45 off 37 balls) and hard-hitting Man of the Match Dewald Brevis, who thrashed 41 off 17 balls, put on 72 for the fourth wicket to ensure a comfortable win.
HIGHLIGHTS: Zimbabwe vs Proteas (Tri-Series T20I)
Proteas captain Rassie van der Dussen praised the two young batsmen.
“There was a little bit of pressure up front,” he said. “Losing three wickets in the powerplay was not ideal but their partnership was brilliant.”
Brevis hit five sixes and a four in his innings, including three successive sixes off leg-spinner Ryan Burl.
Raza said Ngarava, who took 3-35, and Gwandu (3-15) were outstanding.
“It was the first game of the winter [in Harare] and we weren’t sure of the wicket,” said Raza of his team’s batting performance. “At least we know these are going to be high-scoring games.”
© Agence France-Presse
