Japan's former world number one, now ranked 73, defeated Lucia Bronzetti of Italy 6-3, 6-2 and next faces 21st seed Yulia Putintseva of Kazakhstan.
Osaka said this month she was splitting with Belgian coach Wim Fissette.
There has been no official announcement of a tie-up with the renowned French coach Mouratoglou, but he was pictured arriving in Beijing with Osaka.
They were also seen practicing in the Chinese capital ahead of her first-round match against the 77th-ranked Bronzetti.
Fissette had two stints coaching Osaka, from 2019 to the summer of 2022 and again when they reunited last year as Osaka launched her return to tennis after the birth of her daughter Shai in July 2023.
Osaka has struggled to put together victories since she returned to the WTA Tour in January.
She bowed out in the second round of the recent US Open and her best results since returning to action have been two quarter-final appearances.
Osaka won the China Open in 2019.
