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Pakistan were on track to overhaul South Africa's 188 for three until Azam was out off the first ball of the 17th over.
Set 321 to win after David Miller and Faf du Plessis hit centuries, Australia could only manage 280-9 off their 50 overs despite a battling 106 from Shaun Marsh.
The series is all square with the Proteas winning the opening game by six wickets and Australia snapping their seven-game losing streak to clinch the second by seven runs.
Set 232 to win, the Proteas could only manage 224-9 in their 50 overs, leaving the series tied at 1-1 with the decider in Hobart on Sunday
David Miller has scored 3,342 runs in 63 first-class matches, averaging 36.32 with six centuries and 19 half-centuries.
Dismissing de Villiers and David Miller with their brilliant fielding, Team India enjoyed a huge boost in confidence.