In reply, South Africa reached 154-7 as Devine took three wickets to make it 100 for her T20I career and three other bowlers snared a scalp.
Hayley Jensen's run out from her own bowling of the dangerous Chloe Tryon (39 off 17) dealt a death blow to the South African chase in the 16th over.
Bates also took a nice tumbling catch at mid on to remove key batter Laura Wolvaardt in the 13th over, completing a player-of-the-match display for the 34-year-old.
The result was crucial for a Ferns side featuring three T20I debutants, given the nature of the competition. With hosts England and Sri Lanka also in their pool, the Kiwi side now need only one more victory in their next two games to reach the medal round.
The victory also made for a good start to the reign of new coach Ben Sawyer, the Australian who was appointed to replace Bob Carter after the White Ferns failed to reach the knockout rounds of their home ODI World Cup earlier in the year.
This tournament marks the first appearance of women's cricket at the Commonwealth Games and the return of the sport after men played a 50-over event in 1998.