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Top seed Serena eased to a 6-3 6-2 triumph over teenage qualifier Lisa Pigato in the highlight of Monday's action in the clay-court tournament, wrapping up the result in 68 minutes.
Pigato, 17, was making her debut in the main draw of a professional event having come through qualifying in Parma.
She enjoyed early success against the legendary Williams, too, claiming a break of serve in the opening game, but the 23-time grand slam champion soon got to grips with the task at hand.
"The first game, she played really good and I needed to adjust to get back," Serena said afterwards. "It was a bit of both, figuring out her game as well."
Next up for the American, who accepted a wildcard into the event after an early exit at the Internazionali BNL d'Italia in Rome last week, will be Katerina Siniakova, a 6-1 6-3 winner over Clara Tauson.
Venus, however, failed to make it beyond her opening outing, losing out to Anna Karolina Schmiedlova despite taking the opening set.
The Slovakian made it four wins in five meetings against the seven-time major champion, eventually prevailing 5-7 6-2 6-2 after two hours and 39 minutes on court.
Elsewhere, Sloane Stephens defeated fellow American Caty McNally in two sets, while seventh seed Sara Sorribes Tormo overcame Bernarda Pera 6-4 6-2.
There was also a win in straight sets for eighth seed Caroline Garcia, who got the better of Paula Ormaechea in a contest that saw both players serve impressively.