Australia secured a first-innings lead of 74, skittling the Proteas for 138 midway through the second session of day two on Thursday.
But after his 5-51 in the first innings, Proteas spearhead Kagsio Rabada (2-15) stepped up again to claim Usman Khawaja (six) and Cameron Green (0) in a three-ball burst just before tea.
Australia finished the session on 2-32, with new opener Marnus Labuschagne on 16 not out and Steve Smith unbeaten on four, with the lead out to 106.
Victory in only the third WTC final would ensure Australia have landed four ICC trophies since November 2021.
But South Africa are refusing to throw in the towel, having not won an international title since the 1998 Champions Trophy.
The evergreen fast-bowling machine of Cummins, Josh Hazlewood, and Mitchell Starc proved too good for the batting of South Africa, who ended the WTC cycle on top of the table.
While Starc started the destruction on Wednesday evening, Cummins (6-28) was relentless in finishing the job.
It was the 14th five-wicket haul of Cummins' brilliant 68-Test career.
The first paceman to captain Australia long-term, Cummins joins the country's greats in reaching 300 wickets.
Shane Warne (708 wickets) and Glenn McGrath (563) sit one and two, while Cummins' teammates Nathan Lyon (553) and Mitchell Starc (384) are next in line.
Dennis Lillee (355), Mitchell Johnson (313) and Brett Lee (310) are the others to take more than 300.
Out of those eight, only McGrath has a better average (21.64) than Cummins' 22.08.
"It's way more than I could've asked for," Cummins said.
"For any fast bowler, 300 is a big number, it means you've battled a few injuries and niggles and got through it."
The 32-year-old also finished with the best figures by a captain at Lord's, bettering England's Bob Willis' 6-101 in 1982.
One of Cummins' six victims was Kyle Verreynne, who had to go after being trapped lbw.
As Cummins was pedalling backwards while appealing, he and Verreynne collided with each other and tumbled over.
The umpire gave the South Africa wicketkeeper not out, but Cummins successfully appealed.
Starting day two in serious trouble at 4-43, the Proteas were able to frustrate Australia's star-studded bowling attack in the first session and move to 5-121 at lunch in pursuit of 212.
But Cummins inspired a collapse of 5-12 to end the innings in a hurry.
David Bedingham (45) top scored for South Africa, while Proteas captain Temba Bavuma survived a controversial DRS decision.
Adjudged lbw on 16 off Josh Hazlewood, Bavuma left it late to review, but eventually took the decision upstairs with four seconds remaining.
The ball would have been smashing into the stumps, but a spike on snicko incredibly meant Bavuma had survived.
Former England captain Alastair Cook said during radio commentary he didn't believe Bavuma had hit it.
But after looking promising, highlighted by pulling opposing captain Cummins for six, Bavuma (36) scooped a drive to cover where Marnus Labuschagne pulled off a terrific diving catch.
This AAP article was made possible by support from Amazon Prime Video, which is broadcasting the World Test Championship final.
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