Warner was unbeaten on 67 from 56 balls and having reached 98 for one in the 13th over, Australia looked odds-on for the victory until South Africa found a way to cut off the boundaries and they finished short on 146 for six.
The series is level at 1-1 with the decider to be played in Cape Town on Wednesday, after which the sides will contest three one-day internationals.
"We've played here a number of times and I've realised that the new ball is key," South Africa captain Quinton de Kock said at the post-match presentation.
"We understand that this wicket, especially late afternoon, for the team batting second it's always going to be difficult."
De Kock was again the mainstay of the South African innings, his clean striking bringing five fours and four sixes in a fine 70 from 47 balls before he holed out to mid-off.
Rassie van der Dussen (37 from 26 balls) provided a vital contribution, but South Africa were 20 or so runs short of where they should have been, having scored only 36 runs in the last five overs with wickets in hand. Seamer Kane Richardson was the pick of the Australian bowling attack with 2-21 in four overs.
Australia appeared to be cruising in their reply and when Steve Smith (29 from 26 balls) was out with the score on 98, they required 61 from 45 balls with eight wickets remaining.
But South Africa used the slow wicket expertly as leg-spinner Tabraiz Shamsi returned figures of 0-17 in his four overs to increase the pressure on the visitors.
Australia needed 20 from the final 12 balls and when Kagiso Rabada's penultimate over went for only three, they were firmly on the back foot and never recovered momentum.
"I thought we were in the hunt for most of the chase. We just didn't get that kick at the end that we needed," Australia skipper Aaron Finch said.
"Both teams bowled well at the end, it's not ideal but a great game."
Scoreboard
=========================================== South Africa =========================================== Q. de Kock c Starc b Zampa 70 R. Hendricks c Agar b Richardson 14 F. du Plessis c Richardson b Cummins 15 H. van der Dussen c Agar b Richardson 37 D. Miller not out 11 P. van Biljon not out 7 Extras: (lb3, w1) 4 =========================================== Total: (4 wkts, 20 overs) 158 ===========================================
Fall of wickets: 1-60 (Hendricks), 2-81 (Du Plessis), 3-121 (De Kock), 4-147 (Van der Dussen)
Bowling: Starc 4-0-38-1 (1w), Cummins 4-0-31-1, Richardson 4-0-21-2, Zampa 4-0-37-1, Agar 4-0-28-0
Did not bat: D. Pretorius, K. Rabada, A. Nortje, L. Ngidi, T. Shamsi.
=========================================== Australia =========================================== D. Warner not out 67 A. Finch b Ngidi 14 S. Smith c Du Plessis b Pretorius 29 A. Carey b Ngidi 14 M. Marsh c Miller b Ngidi 6 M. Wade c and b Rabada 1 A. Agar b Nortje 1 M. Starc not out 2 Extras: (b1, lb7, nb1, w3) 12 =========================================== Total: (6 wkts, 20 overs) 146 ===========================================
Fall of wickets: 1-48 (Finch), 2-98 (Smith), 3-124 (Carey), 4-138 (Marsh), 5-139 (Wade), 6-143 (Agar)
Bowling: Rabada 4-0-27-1 (1w), Nortje 4-0-24-1, Ngidi 4-0-41-3 (1nb, 2w), Pretorius 4-0-29-1, Shamsi 4-0-17-0
Did not bat: P. Cummins, K. Richardson, A. Zampa
Result: South Africa won by 12 runs
Series: The three-match series is level at 1-1
Toss: South Africa
Umpires: Bongani Jele, Allahudien Palekar (both RSA)
TV umpire: Adrian Holdstock (RSA)
Match referee: Andy Pycroft (ZIM)
Remaining match: February 26, Cape Town.