Tim David scored a blistering 83 from 52 balls
Josh Hazlewood took 3-27 and Ben Dwarshuis 3-26.
The second of the three-game series is in Darwin on Tuesday
Australia held off South Africa for a 17-run victory in the first of three T20Is, with Tim David continuing his red-hot form by smashing 83 runs off 52 deliveries.
The Proteas' trip Down Under, which will also comprise three ODI matches, began in Darwin and started well enough as Australia were dropped to 30-3.
Kagiso Rabada had the returning Travis Head (two) and Mitchell Marsh (13) caught in the early stages, while Josh Inglis was dismissed by George Linde for a golden duck.
And when Cameron Green, Mitchell Owen (two) and Glenn Maxwell (one) followed by the end of the eighth over, the former having hit a rapid 35 off 13 balls, Australia looked to be in trouble.
But from 75-6, Australia reached 178 before being all out from the final ball of the innings, with David spending an hour and 14 minutes at the crease before he was finally caught by Tristan Stubbs off Kwena Maphaka's bowling as he finished with figures of 4-20.
Like their hosts, South Africa made an inauspicious start with the bat and were dropped to 48-3, with Josh Hazlewood removing Aiden Markram (12) for the first of three wickets on his return to the squad, having been rested for the recent tour of the West Indies.
Ryan Rickelton's stubborn 71 off 55 balls gave the tourists a chance, but when Hazlewood captured two wickets for one run in a spectacular 15th over, Australia were on top.
With South Africa needing 21 runs off five balls to pass their target, Ricketon's resistance was ended by a scarcely believable catch from Maxwell, who jumped over the boundary to claim the ball, released it back over his shoulder before landing, then leapt back into bounds to grasp it again.
South Africa reached 161-9 in the end, also seeing Rabada bowled by Ben Dwarshuis off the final ball, as the Australia bowler finished with figures of 3-26.
Data Debrief: David drives Australia to victory
David entered this series in excellent form, having averaged a six every 3.3 balls hit in T20Is this year – the best rate of any player from a full member nation to play at least two innings.
His 15 sixes were also more than any player from either Australia or South Africa, and he plundered another eight here, in addition to four fours.
Australia now know victory in Tuesday's second T20I will secure a sixth consecutive series win over South Africa in the format. The Proteas' only victory over them in a multi-game series in the format came in March 2009 (2-0).
