The 15-time Grand Slam winner broke Cornet in the first game of the match and was never troubled after that, as she broke the Frenchwoman once more in the first set and twice in the second for a comprehensive victory.
Williams had far too much firepower for Cornet, hitting 25 winners to four including six aces. One in the second set was clocked at 200 kmh (125 mph).
The third-seeded American stepped up a gear from her opening-round win over fellow countrywoman Varvara Lepchenko. “She’s (Cornet) a former top 15 player and we’ve had a tough three-set match before, so I knew I had to play really well. I tried to be more aggressive and tried to be more consistent,” she said.
Former Wimbledon champion Kvitova, who won in Brisbane in 2011, went down 6-4, 7-5 to Russia’s Anastasia Pavlyuchenkova, while Italy’s Errani lost in three sets to 2012 runner-up Daniela Hantuchova 4-6, 6-1, 7-5.
“It wasn’t my best tennis today and I think that it’s the beginning of the season, so I hoped that it could be better, for sure,” Kvitova said.
“Right now I have still some space where I can improve and I hope that in Melbourne I will improve these things,” she added.
Top seed and World No 1 Victoria Azarenka plays her second-round match against German Sabine Lisicki today.
In the men’s draw, Uzbekistan’s Denis Istomin downed eighth seed Martin Klizan 6-1, 6-2, while Jurgen Melzer, the seventh seed, beat US qualifier Denis Kudla 2-6, 6-4, 6-4.