Starting day three of their second innings 8-144, Australia's plucky lower-order batted for 119 minutes and added another 78 runs during a Test where the bowlers have dominated.
No.11 Josh Hazlewood (17) hung in there for 53 balls and was the last player out on the stroke of lunch, caught in the deep to give part-time spinner Aiden Markram his second wicket of the Test.
Star quick Mitchell Starc (58 not out), batting at No.9, finished as Australia's top-scorer of the innings ahead of wicketkeeper Alex Carey (43).
Starc faced more balls than any other batter during an innings in this Test, even more than Steve Smith's 112 for his 66 on day one.
It was the 11th fifty of Starc's 97-Test career, but could be his most significant innings.
If the match goes down to the wire, South Africa will be left to rue bowling 20 no-balls during the Test.
Star Proteas quick Kagsio Rabada (4-59) finished with match figures of 9-110 after he destroyed Australia with 5-51 in the first innings to put his name on the Lord's honour board for a second time.
"It would have been nice to get a 10-for, but I'd rather a win than a 10-for," Rabada said at lunch.
To win their first ICC title since 1998, South Africa would need to post the highest total of the Test.
They would need to pull off the equal second-highest successful chase in a Test at Lord's, with England running down 282 against New Zealand back in 2004.
Back in 1984, West Indies in their prime successfully chased 342 against England at the famous ground.
Australia, inspired by six wickets from Pat Cummins, rolled South Africa for 138 on Thursday.
But the reigning champions fell into deep trouble in their second innings when they collapsed with 5-29 during a frantic 45-minute period.
Victory in only the third edition of the WTC final would ensure Australia have landed four ICC trophies since November 2021.
Fourteen wickets tumbled on Thursday, after 14 had already fallen on a dramatic opening day.
Australia will back in their fearsome, experienced pace battery after Cummins, Starc and Hazlewood.
While Cummins grabbed most of the wickets in the first innings, Starc and Hazlewood were relentless with their line and length.
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