The 45-year-old has not tasted victory on a singles court since the first match of her latest comeback in Washington last summer, and her fortunes did not change as she stepped back on clay.
Williams was giving away 25 years to Quevedo in her first match on the surface since the French Open in 2021.
The veteran briefly threatened to make it a real contest when she led 3-0 in the second set but Quevedo hit back to claim a 6-2 6-4 victory – her second on the WTA Tour.
"I felt like in the last game I started to move better on the clay," said Williams. "But then it was the last game.
"All these things take adjustments. I started my practice on clay a couple of weeks after Miami. I haven't really played on clay in years. But I enjoy the clay, it's fun. I played against a very inspired opponent today.
"The conditions weren't easy for both of us, so much wind and rain and interruptions in the match. I don't think that was helpful."
Williams has stuck firmly to hard courts when she has played in recent years, and this was her fourth appearance at the Caja Magica since her most recent victory, which came back in 2012.
She took time to find her feet but produced some fine shots at the start of the second set before windy conditions knocked her off her rhythm, with the roof eventually shut for rain as a thunderstorm hit Madrid.
Williams' stay in the Spanish capital is not over yet, with the American accepting an invitation from Britain's Katie Boulter to play in the doubles tournament.
Williams would need another wild card if she is to make her return to Roland Garros, and that appears to be a prospect she would relish, although she will definitely miss the Italian Open next month.
Among other ties in the first day of main draw action in Madrid on Tuesday Jessica Bouzas Maneiro beat Beatriz Haddad Maia, Paula Badosa lost to Julia Grabner and Laura Siegemund defeated Irina-Camelia Begu.
Australia's Tahlia Gibson starts her tournament Wednesday against Colombia's Emiliana Arango, ranked 86.
Daria Kasatkina, Kim Birrell, Ajla Tomljanovic are also in the event.
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