The 24-year-old will face sixth-seeded Daria Kasatkina of Russia in the title clash.
The tie-break will be used only once the score in the deciding set reaches 12-12.
In September, Serena was warned for coaching when Mouratoglou was spotted making signals from the players box during the US Open final against Naomi Osaka.
Kyrgios's injury meant that Bosnia's Mirza Basic got a free pass into the quarterfinals where he will take on Russian Karen Khachanov.
The Barcelona defender is also the president and founder of Kosmos, the company promoting the new Davis Cup.
The duo joined top-ranked Simona Halep, Angelique Kerber, Naomi Osaka, Petra Kvitova, Caroline Wozniacki and Sloane Stephens.
Damir Dzumhur's title defence came to an abrupt halt with a first-round loss to Belarusian qualifier Egor Gerasimov.
Wim Fissette, the former coach of Kim Clijsters (2009–11), current world number one Simona Halep (2014) and Victoria Azarenka (2015–16), joined forces with Kerber in November 2017.
The 27-year-old's appearance in Moscow and the WTA Finals had been in doubt when she withdrew from Beijing two weeks ago and was diagnosed with a herniated disk in her back.
This year Halep has won the Shenzhen Open, the Rogers Cup and her debut Grand Slam crown at Roland Garros.
After his 6-3, 6-4 victory over Borna Coric in the Shanghai final on Sunday, Djokovic is just 215 points behind the Spaniard.
Del Potro has been plagued by injuries since winning his only Grand Slam title at the 2009 US Open at the age of 20.
The 26-year-old Italian is set to rise to a new career-high ranking on Monday from her current position of 32.
The 31-year-old will leapfrog Roger Federer into second in the world when the rankings are released on Monday.
The 18-year-old Ukrainian comprehensively outplayed the world number 24 Wang Qiang to win the tournament without losing a set all week.