The unseeded Jovanovski hit 33 winners to only 13 for the 10th-seeded Dane. She will next face former French Open champion Svetlana Kuznetsova of Russia.
A runner-up at the 2009 U.S. Open, Wozniacki had her best showing at Roland Garros in 2010 when she reached the quarterfinals.
Playing the day's final match on center court, Williams committed only nine unforced errors never faced a break point. Through two rounds she has lost only four games.
The No. 1-ranked Williams seeks her first French Open title since 2002. She hasn't reached the semifinal since 2003.
Since losing in the first round a year ago at Roland Garros, Williams is 69-3, including titles at Wimbledon, the U.S. Open, the London Olympics and the season-ending WTA Championships.
Meanwhile, Victoria Azarenka waited until the fourth day of the French Open for her opening match, then showed she's eager to advance.
Filling a mostly empty stadium court with her familiar shrieks Wednesday, the world's former No. 1 player beat Elena Vesnina of Russia 6-1, 6-4 in a match postponed one day because of rain. That meant Azarenka reached the second round 72 hours after some players.
"I felt like I'm one of the last ones to start," she said. "It was a long wait, but I think performance-wise it was a good match."
The Australian Open champion in each of the past two years, the No. 3-seeded Azarenka is hoping for a breakthrough at Roland Garros, the only major where she has yet to reach a semifinal.
American women went 10-5 in the first round, including Jamie Hampton's first career French Open victory, an upset of No. 25 Lucie Safarova 7-6 (5), 3-6, 9-7. Hampton hit seven aces and overcame 50 unforced errors to outlast Safarova in the 2½-hour match.
"A couple years ago, we weren't even in the scene," Hampton said. "There wasn't even a group of us. We've progressed, and I think the whole group will continue to progress. We've all got really good games. We're just trying to find our way on the clay right now."
Stumbling in the second round was American Mallory Burdette, who lost to No. 4-seeded Agnieszka Radwanska 6-3, 6-2. Burdette committed 28 unforced errors to five for Radwanska, last year's Wimbledon runner-up.
Azarenka waited in vain to play for much of the day on a rainy Tuesday,\ but said she wasn't flustered by the delay.
"I just really was chilling the whole day, watching 'The Voice,'" she said. "It was incredible. I was so entertained. There's this girl, her name is Judith. She was a duet singer with Michael Jackson. She's absolutely incredible. I mean, I have no idea how sounds like that can come out of somebody's mouth. It's just, wow."
Fans might say the same thing about Azarenka, who wore down Vesnina with her noisy but steady baseline game, committing only 13 unforced errors. Vesnina, ranked 38th, fell to 1-19 against top-five players and has yet to take a set in five matches against Azarenka.
Azarenka needed only half an hour to win the first set, fell behind in the second, then finished with several booming strokes and a fist pump. Addressing the crowd afterward, she tried to match rival Serena Williams' feat of speaking French to the spectators, but stumbled.
"I know 'Je t'aime, Paris,' and I know 'Allez,'" she told the fans with a laugh. "Merci beaucoup."
Later, Azarenka said she doesn't mind the heavily favored Williams being the focus in the women's draw.
"Serena always has attention, no matter where she is," Azarenka said. "She has been around the game so much and the No. 1 player in the world. It's usual. For me it's important to show up for my job. Whatever is going on around, it's just entertaining for people. But I'm just focused on what I do and nobody else, really."
In other first-round matches, No. 7 Petra Kvitova outlasted wild card Aravane Rezai of France, 6-3, 4-6, 6-2, and No. 12 Maria Kirilenko beat fellow Russian Nina Bratchikova 6-0, 6-1. No. 23 Klara Zakopalova lost to Kaia Kanepi 7-6 (3), 6-2.
Information from The Associated Press was used in this report.