The World Cup was finally treated to the supreme batting feat that it craved yesterday when Steve Waugh thrust Australia into the semi-finals in defiance of a South African juggernaut that had brought them to the brink of collapse.

Only three balls remained when Waugh, with virtually his only false stroke in three phenomenal hours, edged Shaun Pollock to the third-man boundary. The captain had dragged Australia home by five wickets. When the elation subsided, even he must have shuddered at the thought that they must now beat South Africa again at Edgbaston on Thursday.

No cricketer evokes more admiration than Waugh, no one is more renowned for their immense mental strength; but, even by his standards, the match-winning hundred which held the tournament favourites at bay was extraordinary. The discriminating strokeplay, the calculating mind, and more bottle than a morning milk float: these are the strengths that have made Waugh the most redoubtable of modern Test batsman.

In one-day cricket, the mix has been less potent, with only one previous century in 265 attempts. But when it mattered his unbeaten 120, from 110 balls, responded to every need.

For Herschelle Gibbs, whose own hundred had promised South Africa victory, Waugh's triumph will fester long in the memory. When Waugh, on 56, clipped Lance Klusener in front of square, Gibbs collected it with the ease befitting one of the finest fielders in the world, only to fling it away in his desire to throw it up in celebration.

As Waugh survived a last-ditch assault from Allan Donald, with 15 still needed from two overs, a few stretching exercises to awaken stiffening limbs served as a reminder that, only a few weeks ago, his one-day retirement was being widely forecast.

At 48 for three in the 12th over, facing a daunting South African total of 271 for seven, an Australian victory seemed highly improbable. Stories of Australian never-say-die attitudes abound, but all that seemed negated by the threat of a high-class South African attack on a slightly uneven pitch.

Adam Gilchrist, beaten by Elworthy's low bounce, had again proved vulnerable to the ball angled back into him; Mark Waugh, drawn into an unlikely single by Rickie Ponting, had been run out by Nicky Boje; Damien Martyn fell hooking. Zimbabwe, watching on TV, must have imagined their semi-final place secured.

But the absence of Jacques Kallis, with an abdominal strain, left South Africa's fifth bowler more vulnerable than usual, and Waugh not only identified the weakness, but exposed it mercilessly. The left-arm spin of Boje, in his second game of the tournament, and Hansie Cronje's medium pace went for 79.

Ponting, driven on by self-recrimination, finally produced the significant innings that he has threatened for the past month, 69 from 110 balls in a stand of 126. Michael Bevan, the best finisher in the world, added 27 from 33 balls, but appropriately left Waugh to apply the final gloss.

Gibbs, his reputation blossoming, had organised South Africa's innings with 101 from 134 balls, coming to grief five overs from the end when he was yorked making room against Glenn McGrath. Gibbs launched Paul Reiffel into a confectionery stall, and Jonty Rhodes deposited him onto the roof of the Yorkshire club offices. But, almost unnoticed, a personal renaissance was keeping Australia in the match.

Shane Warne's two for 33 rescued a personal World Cup fraught with uncertainty. Just as five overs for 44 against Zimbabwe at Lord's led him to worry about his future, so his success yesterday will persuade him that he can recapture past glories.

Warne made good use of a pitch offering slight turn, bowled Cullinan in his penultimate over as he tried to sweep a leg-break, then had Cronje leg before to the same shot three balls later. Warne fell gratefully to his knees and punched the air as if close to exhaustion.

Rarely, also, can Warne have held such an outstanding catch as the last-over effort that dismissed Klusener, who lashed 36 from 21 balls before his sliced drive at Damien Fleming was brilliantly snaffled by Warne as he dashed backwards from extra cover, especially as he had dropped Klusener off McGrath in the previous over.