The eighth-wicket partnership yielded 50 from just 22 balls including three sixes and six fours, with Theron fittingly smashing David Hussey into the stands for the winner with five balls to spare.
It was a crushing defeat for the Australians who appeared destined for a series clean sweep when South Africa slumped to 84 for 7 after 14.4 overs in reply to their total of 147 for 7.
In the crucial death overs it was Doug Bollinger (1 for 36), Stephen O'Keefe (1 for 35) and youngster Pat Cummins (2 for 26) who took the biggest pounding, as Parnell and Theron brought the capacity crowd at The Wanderers to their feet.
White said his men were shattered after blowing an opportunity to wrap up the series, but believes his young troops will be better for the heartache.
'It's a really hard one to swallow I guess. You should get over the line there most times,' White said at the post-match press conference.
'In saying that it'll be a great learning curve and experience for our young team. You can't get practice or circumstances like that other than what they've just experienced.'
One of those young players, Cummins bowled brilliantly early in the innings and looked to have put Australia in the winning position with a tightly executed 2 for 3 in his initial spell.
But he learned in the 19th over just how brutal Twenty20 cricket can be, giving up 13 runs as the South Africans charged.
For Parnell, his fine innings was redemption, after he was pumped for 44 runs with no success from his bowling spell.
While clutch-hitting hero Theron was a clear man of the match after also taking two wickets.
'I think it's very hard to describe, not something that's really sunk in, it's one of those rare occasions where I find myself a little speechless,' said Theron.
'I can just be thankful for an opportunity like that to come along where you can do something special.'
Mitchell Marsh was a late inclusion for Australia vice captain Shane Watson, who pulled out with a hip strain, and helped make up for a patchy batting display which began with a second consecutive duck for David Warner.
Marsh's powerful cameo (39 off 26) lifted Australia from a precarious position.