Murray came from a break down in each set to beat world No. 13 Matteo Berrettini — a semifinalist at last month’s US Open — 7-6 (7-2) 7-6 (9-7) — as he continues his comeback on the singles circuit.
The three-time grand slam champion, who underwent career-saving hip surgery in January, made a tentative return to singles in Cincinnati in August but has been unable to progress past the round of 16 in four previous tournaments.
No. 4 seed Osaka, who won a title in her home city of Osaka last month, brushed past qualifier Andrea Petkovic 6-2 6-0 in Beijing.
The 59-minute win extends the 21-year-old’s winning run to six matches.
The former world No.1 hit five aces and 21 winners on the way to a comfortable victory, in which she faced only one break point — which she saved.
The Japanese star cited her change in coach as a key reason for her uptick in success.
Osaka split from coach Jermaine Jenkins — who in turn replaced Sascha Baijin, the mentor behind her two grand slam titles — after the US Open and is now working with her father, Leonard François.
“It took me back a little bit because he’s always been around, but he’s been in the shadows for the most part,” she said after the win.
“I would say he is a person that knows my game the most. He’s kind of the person that knows the trigger words, whether good or bad.”
After winning the Australian Open in January, Osaka has had a disappointing year, being knocked out before the quarterfinals stage in all other grand slams.
The 2018 US Open champion will face either Alison Riske or Ajla Tomljanovic in the third round.