In response to the Proteas’ 172-7, Australia were in trouble at 122-6 in the 14th over before Maxwell stepped up with an unbeaten 62 off 36 balls.
There was a late twist when Proteas quick Corbin Bosch dismissed Ben Dwarshuis and Nathan Ellis with consecutive deliveries. But Maxwell crunched a boundary on the penultimate ball of the match before celebrating with gusto.
Hot favourites Australia won the first match but were stunned by a 52-run defeat in game two before moving to Cairns in northern Queensland, which hosted its first T20I.
“It was a little nerve-racking,” Maxwell said. “I tried to stay on strike as much as I could and cash in on anything loose.”
HIGHLIGHTS: Australia vs Proteas (3rd T20I)
Australia captain Mitchell Marsh elected to field in helpful conditions for seam bowlers, a contrast to the batting-friendly surfaces used in the opening two games in Darwin.
Veteran quick Josh Hazlewood rebounded from an errant performance in game two by dismissing captain Aiden Markram for one in the first over.
Lhuan-dre Pretorius hit a quick-fire 24 before falling to Ellis, bringing to the crease Dewald Brevis who smashed a South African T20I record of 125* in game two.
He crunched his sixth delivery onto the roof before a diving Maxwell dropped a tough one-handed chance at long-on.
Brevis motored to his half-century off 22 balls.
Maxwell, a brilliant fielder, redeemed himself in the 12th over with a superb diving catch in the outfield to halt Brevis’ charge on 53.
The Proteas’ innings ran out of steam and their total appeared well short when Marsh dominated a 66-run opening partnership with Travis Head.
But South Africa hit back with the quick wickets of Head (19) and Josh Inglis for a first ball duck.
Marsh made 54 before holing out to 19-year-old quick Kwena Maphaka, who later in the 11th over dismissed Cameron Green (nine).
Australia’s collapse of 6-56 was complete when in-form Tim David (17) and Aaron Hardie (one) were dismissed before Maxwell took over.
The Australian players wore black armbands in honour of former captain and coach Bob Simpson, who died at the age of 89.
The three-match ODI series between the teams starts in Cairns on Tuesday.
