Australian fast bowler Glenn McGrath's triple strikes, including two wickets off successive balls, had half the batsmen back in the pavilion within the first 10 overs before South Africa were routed for their lowest World Cup total of 149.
The world champions eased to 153 for three in the 32nd over, setting up a final against 1996 champions Sri Lanka in Barbados on Saturday.
"I don't think we played reckless shots and threw wickets away," coach Mickey Arthur told a news conference. "We needed to disrupt Australia's momentum somehow and get on top and needed to get on top quick."
Captain Graeme Smith added: "We pride ourselves on these big days but we didn't play well.
"I definitely don't think we choked," he added. "We just weren't good enough. We were outplayed and you have got to give credit (to Australia).
"The top order just got out to good bowling, maybe one or two loose shots."
Smith himself was guilty of throwing his wicket away when the left-handed opener was bowled attempting a wild shot against paceman Nathan Bracken in the third over.
South Africa, desperate to reach a maiden World Cup final, never really recovered after they were reduced to 27 for five in the 10th over with fast bowler Shaun Tait complementing McGrath to finish with four wickets.
Jacques Kallis, usually the innings anchor, was also bowled trying a big shot against McGrath, who then had Ashwell Prince caught behind for a second-ball duck chasing a wide delivery.
"Our top order has played quite positive throughout the tournament," Smith said. "The ball did swing a bit up front which they used to their advantage.
"Once we became three down it became really difficult to wrest the initiative back."
South Africa have now been knocked out in the semi-final in three of the last five editions.
