The 45-year-old Williams, playing on a wildcard at the prestigious ATP/WTA Masters 1000 event, rallied from a set and a break down to force a third set, but Parry, ranked 111th in the world, stormed through the decider for a 6-3, 6-7(4), 6-1 triumph.
"It's always so fun," Williams said. "Of course, losing isn't fun, but it's great to play in front of a home crowd."
While the Californian star is enjoying competition since returning last July from a 16-month hiatus, Williams was mum on the chances fans would see her and sister Serena play together this year.
"You'll have to ask her that," Williams said to the question that has bubbled in the tennis world since 23-time Grand Slam champion Serena re-entered the anti-doping testing pool.
While Williams remains in search of her first win of the year after first-round exits at the Australian Open and in Austin, Texas, she said Thursday's game wasn't a good gauge of her game.
"I think today is not the kind of day that you want to assess," she said. "The conditions are impossible. Also, my match in Austin the conditions were impossible.
"In Austin I refused to relent and change my game and I lost very quickly. Today I tried to adjust. It's not easy. You can't trust anything that you do out there."
The 23-year-old Parry, who was born after Williams had won the first four of her Grand Slam titles, said despite the conditions she could feel the force of Williams' game.
"Even if it wasn't pretty tennis today because of the wind, you can still clearly see the quality of her shots - forehand, backhand - as soon as she gets a ball she can attack, there's little chance you're getting it back.
"You can imagine what it was like when she was at her best," said Parry, adding it was "an honour to be able to play against a legend of our sport.
"I watched more of Serena, the greatest player of all time, but I think a lot of people forget the career that (Venus) has had.
"When, during the warm-up, the announcer gave a brief summary of her career, you think, 'Oh right, that's really something.'"
'Solid'
In men's first-round action, Bulgarian veteran Grigor Dimitrov booked a second-round meeting with top-seeded Spaniard Carlos Alcaraz with a 6-4, 5-7, 6-4 grudge match victory over Terence Atmane, who had beaten the former world number three in Acapulco last week.
"I think I started the match really well, but it was just difficult to maintain a solid level," Dimitrov said. "It could have gone either way, but I was able to stay very strong in the most important moments."
Dimitrov, a 2021 Indian Wells semi-finalist, now gets a shot at Alcaraz, who is undefeated in 12 matches in 2026 and beat Dimitrov in the fourth round here last year.
Alcaraz, whose Australian Open triumph in January made him at 22 the youngest man to complete a career Grand Slam, will launch his bid for a third Indian Wells title on Saturday.
Second-seeded Jannik Sinner of Italy launches his campaign for a first Indian Wells title on Friday, headlining the night session against Czech qualifier Dalibor Svrcina.
Fourth-seeded German Alexander Zverev will open second-round play on Stadium Court on Friday against Italian Matteo Berrettini, with women's world number one Aryna Sabalenka up next against Japanese qualifier Himeno Sakatsume.
Like Sinner, Sabalenka is chasing a first Indian Wells title. She fell in last year's final to Russian teen Mirra Andreeva and in 2023 to Kazakhstan's Elena Rybakina.