Putintseva, ranked 46 in the world, reached the quarter-finals with a 6-2 6-3 victory in one hour and nine minutes.
Osaka looked out of sorts all match, dropping serve three times in each set and saving just four out of 10 break points.
The reigning US and Australian Open champion also won just 51% of her first serves and that dropped to 24% on her second serves.
She is yet to advance beyond the third round at Wimbledon, and she will lose her spot at the top of the rankings should Ashleigh Barty win the tournament.
Australian Barty safely reached the quarter-finals with a 6-3 6-1 victory over Jennifer Brady in just over an hour.
Putintseva meanwhile recorded her fourth victory over a world number one, and she will face Julia Goerges in the next round.
Goerges, seeded eighth, overcame Evgeniya Rodina 6-4 6-3 on Thursday.