Proteas skipper Quinton de Kock had already cleared the rope three times when he thumped an Adam Zampa delivery over deep mid-wicket, only for Smith to launch himself over the rope and throw the ball back before landing to save the six.
Smith almost did it again to dismiss Miller off the final ball of the innings but spilt the juggling effort when he tripped over the boundary rope.
"That's superman ... that is absolutely unbelievable Steve Smith," one of the commentators said.
"So many would just give that up because they've literally got no chance. If anything, you've got one per cent chance. That is out of this world."
His co-commentator added: "It's astonishing. Absolutely astonishing."
It was a comeback for the ages after the Proteas were humiliated in Johannesburg — bowled out for just 89 in a record 107-run defeat.
The series-decider will be played in Cape Town on Thursday morning AEDT.
De Kock (70 off 47 balls) was the hero with the bat in Port Elizabeth but it was in the field where South Africa were truly redeemed.
Faf du Plessis and David Miller combined for an outrageous relay catch on the boundary to see off Mitch Marsh, while quicks Lungi Ngidi (3-41), Nortje and Kagiso Rabada all delivered inspired performances in the final overs.
Australia gambled on promoting Carey to No. 4, backing his batting against spin with crafty left-arm tweaker Tabraiz Shamsi controlling the tempo. Carey was bowled by Ngidi for 14 and neither Marsh nor Wade made it past single figures.
"Sitting back there now, I think the players will feel it's a missed opportunity to win the series away from home, which is always a huge accomplishment," assistant coach Andrew McDonald said.
"Now we've got our work cut out, a short turnaround to Cape Town and prepare as best we can to perform well there."
Warner and Smith (29) combined for a 50-partnership before du Plessis snared a superb low catch at long on to dismiss Smith off the bowling of Dwaine Pretorius.
