Venus, 42, who won her last match at the Midwestern pre-US Open event in 2019, lost to 2016 champion Karolina Pliskova 7-5, 6-1.
Osaka's summer form slump deepened meanwhile as the four-time Grand Slam winner was defeated 6-4, 7-5 by China's Zhang Shuai.
Pliskova, one of the game's biggest servers, struck eight aces and broke four times in a win over Williams lasting for nearly one and three-quarter hours.
Williams, a semifinalist from a decade ago, has gone winless in her last five matches, last earning a victory in the Wimbledon first round.
Pliskova said she had to lift her level to run away with the second set.
"Venus is a great champion, she's a fighter with a big game and big serve," the Czech said.
"She played well at certain points in the first set, I'm feeling physically strong so I was able to up my game in the second set."
Osaka's first-round defeat was the second in as many weeks for Japan's former world No 1, now ranked 39th.
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