A day after Roger Federer led the list of big names to exit in the second round, the top-ranked Williams never looked in danger against the 100th-ranked French qualifier.
Williams broke twice in each set to set up a match with Japan's Kimiko Date-Krumm, who at 42 became the oldest woman to reach the third round at Wimbledon in the Open era.
Date-Krumm beat Alexandra Cadantu of Romania 6-4, 7-5 to reach the third round for the first time since 1996, when she went to the semifinals.
"She's incredibly inspiring," the 31-year-old Williams said. "She's so fit, she's done so well. I've never played her before. I watched her play when I was super young, growing up."
Date-Krumm is the second-oldest woman to have won a match at Wimbledon after Martina Navratilova, who was 47 when she reached the second round in 2004. She took a 12-year break from tennis before returning in 2008.
"I don't know how she's able to do so well," Williams said.
Whether Williams can keep playing for another decade remains to be seen, but she certainly doesn't show any sign of slowing down in her 30s. The defending champion is looking for a sixth Wimbledon title, and saw her two main rivals -- Maria Sharapova and Victoria Azarenka -- eliminated on Wednesday.
The 19-year-old Garcia is seen as a potential future star, with a game especially suited for grass. But she couldn't force a single break point against the American's strong serve on Court 1.
"She's incredibly promising, she does everything well," Williams said. "Her serve is amazing, so I knew it would be a good match on the grass."
After that wild Wednesday, with seven players retiring or withdrawing with injuries, a sense of normalcy returned to the All England Club.
Sixth-seeded Li Na of China did look in trouble for a while before overcoming a poor second set to beat Simona Halep of Romania 6-2, 1-6, 6-0. Halep's lower back was treated after the first set, but she still dominated the second. Li, the former French Open champ, found her stride again in the third.
"Welcome to the crazy women's tennis tour," Li said.
Other seeds to win included No. 14 Samantha Stosur and No. 18 Dominika Cibulkova. Bernard Tomic of Australia, whose father and coach John Tomic has been barred from tournaments after allegedly assaulting his son's hitting partner, advanced by defeating American James Blake 6-3, 6-4, 7-5.
There was one injury retirement: Michael Llodra of France quit after losing the first set 7-5 against 23rd-seeded Andreas Seppi of Italy.
That was the eighth retirement or walkover of the second round in singles play, equaling the record for a single round at Wimbledon in the Open era. The International Tennis Federation said eight players also quit in the first round in 2008.
The record for a Grand Slam tournament is nine players withdrawing or retiring from the first round at the 2011 U.S. Open.
Later in the day, top-ranked Novak Djokovic was to play Bobby Reynolds of the United States.
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