Top-ranked Novak Djokovic also opened with a straight-sets victory, beating Florian Mayer of Germany, 6-3, 7-5, 6-4. Mayer is a two-time Wimbledon quarterfinalist, losing to Djokovic at that stage last year.
Djokovic took a 3-0 lead in the first set and broke for a 6-5 lead in the second to take control. He served out the match to love before saluting the crowd with a fist pump.
"It was a big pleasure again performing here on Centre Court in front of the packed crowd," Djokovic said. "For the first round, it was tricky. . . . I think [Mayer's] game is really well-suited for grass, so it took a lot of effort."
For Williams, this was a chance to put the focus back on tennis following the verbal jousting with Sharapova over their private lives - and comments about an Ohio rape case for which she had to apologize - and she took full advantage.
As usual on grass, the top-ranked Williams dominated with her hard serve, winning the first set without dropping a point on her service game. Her main weapon let her down only at the start of the second set, when Minella took a 2-0 lead after Williams double-faulted on break point.
She was one point from going down 3-0 but then won 15 of the next 18 points to take a 4-2 lead, and broke again to wrap up the win. Williams is now 68-8 at the All England Club and extended her career-best winning streak to 32 matches, which included her second French Open title.
Kimiko Date-Krumm, 42, had an even easier time. She needed just 44 minutes to complete a romp over Carina Witthoeft, an 18-year-old German making her Grand Slam debut. Date-Krumm is the second-oldest player to win a match at Wimbledon. Martina Navratilova was 47 when she reached Round 2 in 2004.
Home favorite Laura Robson delivered the biggest upset, beating No. 10 Maria Kirilenko, 6-3, 6-4, to become the first British woman to beat a top-10 ranked foe at Wimbledon in 15 years.
In less of a surprise, Arantxa Rus lost - again. The 156th-ranked Dutch player equaled a WTA record by extending her losing streak to 17 straight matches with a 6-4, 6-2 defeat to Russia's Olga Puchkova.
"This year is not a good year for me," Rus said.