In the 67th minute, with South Africa leading 9-8, halfback Fourie du Preez swooped and was headed to the line when the Australian first five-eighths flew in and dislodged the ball.
In a match of grinding intensity, this was a rare highlight. South Africa were hurt badly in the 20th minute when their expert fetcher Heinrich Brussow was forced off with a rib injury, replaced by Francois Louw.
With their ball retention under pressure, the champions failed in this area as Pocock and co dominated.
Many of the Australians jumped in delight as referee Bryce Lawrence ended the match, which may bring the curtain down on a couple of wonderful Springbok careers.
One of the veterans, lock Victor Matfield, was quick to shake Lawrence's hand.
In the 70th minute of the match, Lawrence made the decisive call of the game on a touch judge report, penalising Matfield's locking partner Danie Russouw for knocking Radike Samo's support away at a lineout.
Up stepped James O'Connor to land the slightly angled 40m goal for the 11-9 lead, and Australia then had their best 10 minutes of the half to hang on for the win.
Lawrence also rubbed out a South African try in the 45th minute, a marginal but correct call for a forward pass from Jean de Villiers to Patrick Lambie.
Australia had spent most of the spell camped inside their own half as South Africa, as expected, turned the game into an exhausting tangle of joyless, nailbiting rugby.
The game's only try arrived in the fifth minute, the Springboks' lineout having done its job before Schalk Burger lost possession driving the ball out, Samo gathered, and fed captain James Horwill who struggled over.
O'Connor, an unconvincing goalkicker, took the handy conversion attempt back a good 20m, and after J.P. Pietersen charged early and past O'Connor, the little Aussie skewed the ball wide. Five minutes later O'Connor did goal a penalty awarded after a superb Australian lineout move.
South Africa finally got on the board in the 38th minute through a simple Steyn penalty, he missed from about 60m on halftime, and goaled again early in the second half.
Australia will have to fix a wonky lineout for the semifinal but know they have a turnover specialist supreme in Pocock, who can alter the flow of games.
South Africa had ample opportunity to forge a victory in the second spell. Steyn did land a drop goal to take the lead in the 59th minute, but they squandered other chances.
Peter de Villiers' South Africa have been a team searching for their game for much of this tournament. They didn't quite find enough of it last night, although they had the winning of this quarter-final in their grasp.
Australia 11
South Africa 9