The 22-year-old Brevis scored an unbeaten 125 from 56 balls with 12 fours and eight sixes, propelling South Africa to 7-218 before Australia struggled to 165 in front of another noisy near-capacity crowd.
South Africa's victory has levelled the three-match series at one-all and ended Australia's record nine-game winning streak. The deciding match will be played in Cairns on Saturday before a three-match one-day series between the teams in Cairns and Mackay.
Brevis brought up his century in 41 balls, the second fastest in South African T20 history. It was his first international hundred, having passed 50 once in two Tests and registered a top score of 41 in eight Twenty20 internationals.
He unleashed a series of bold strokes, dominating a partnership of 126 in 9.3 overs with the subdued Tristan Stubbs, who scored 31 in 22 balls as the anchorman. Their 100-run stand came up in 44 balls, with Stubbs contributing 16.
Brevis was given a life on 56 when substitute fielder Matt Kuhnemann misjudged a catch at long on which went over the boundary. Brevis had already hit Glenn Maxwell for successive sixes and hit another after the drop in an over which cost 24.
South Africa's performance was a marked contrast to Sunday's opening match when they failed to chase down Australia's under-par 178. The visitors finished on 9-161 to lose by 17 runs and Brevis made two.
For the second time in the series most of Australia's batsmen underperformed, with Tim David again the standout.
He followed his 52-ball 83 in the first game, which propped up Australia's innings, with a 24-ball 50 on Tuesday, despite being forced from the field earlier in the match holding his right shoulder after unsuccessfully diving to stop a boundary.
The next best score was Alex Carey's 26 from 18 balls batting at No. 7. Carey was flown into Darwin as a late replacement for wicketkeeper Josh Inglis, who was suffering flu-like symptoms.
Mitch Owen had another difficult night, again unable to repeat the big-hitting heroics he produced during Australia's 5-0 T20 clean sweep of the West Indies last month.
After almost being bowled first ball with a yorker he was struck in the grill by a short ball from South Africa spearhead Kagiso Rabada.
On six Owen was bowled swinging at seamer Corbin Bosch. The zing stumps lit up but the bails stayed on. They came off a short time later when he was bowled by Kwena Maphaka for eight from 13 balls attempting another unsuccessful slog.
