Despite dominating possession and playing their characteristic high tempo style, Japan was not able to breakdown the Springbok defence and was restricted to scoring just a single penalty.
The four teams that will contest the 2019 Rugby World Cup semifinals in Japan on 26 and 27 October.
Pace duo Mohammed Shami and Umesh Yadav claimed five wickets between them Monday to put India on the brink of a series whitewash after South Africa crumbled while following-on in the third Test.
The 52-year-old Cheika called time on his five-year tenure Sunday after Australia's dismal World Cup quarter-final exit to England, stung by sharp criticism of his tactics.
Former world number one Murray, who appeared on the brink of retirement after losing in the first round of the Australian Open in January, battled back from a set and a break down to win 3-6 6-4 6-4.
Salah hobbled off late on in the European champions' 2-1 victory over Leicester two weeks ago, but Jurgen Klopp is hopeful he can return for Wednesday's Champions League trip to Genk.
"I knew from the final whistle but I just wanted to give it a bit of time to settle down, talk to my people and then make it clear," Cheika said in video footage released by Rugby Australia.
France, 19-10 ahead at half-time, had Sebastien Vahaamahina sent off for an elbow on 49 minutes but they clung to the lead until Ross Moriarty powered over for the vital try late in the game.
There will be no great achievement to underline his nearly two-year sojourn to the United States, the 33-year-old unable to add to his legacy of twice getting his club into the postseason but never winning a match.
South Africans came out in numbers to support the Springbok match against Japan at the 2019 Rugby World Cup. All images supplied by Cecile Basson.
