Osaka, the 2019 China Open champion, started the contest strongly and raced into the 3-0 lead before closing out the first set with a smash.
The four-time Grand Slam winner then stayed on course by winning the opening two games of the second set, but Timofeeva showed her fighting capabilities to hit back and win five straight games.
Osaka regained her composure in the deciding set though and once again raced into a 5-0 lead, and served out the match to advance into the next round.
After surviving the Timofeeva challenge, the Japanese tennis star is set to face Cincinnati semifinalist and No. 20 seed Sara Bejlek.