Serena Williams stamped her authority on the Brisbane International on Tuesday when she crushed Frenchwoman Alize Cornet 6-2, 6-2. On a day that saw second seed Maria Sharapova withdraw with an injured collarbone and fifth and sixth seeds Sara Errani and Petra Kvitova bundled out, Williams was all business as she disposed of Cornet in exactly one hour.

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," she said. "I tried to be more aggressive and tried to be more consistent."

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." Top seed and world number one Victoria Azarenka plays her second-round match against German Sabine Lisicki on Wednesday.

In the men's draw, Uzbekistan's Denis Istomin downed eighth seed Slovakian Martin Klizan 6-1 6-2, while Austria's Jurgen Melzer, the seventh seed, beat US qualifier Denis Kudla 2-6, 6-4, 6-4. Australian qualifier John Millman set up a second-round clash against Andy Murray when he beat Japan's Tatsumo Ito 6-4, 6-1 and Tommy Robredo of Spain edged American Ryan Harrison 6-4, 7-6 (7/4).In the final match, former world number one Lleyton Hewitt of Australia downed Russia's Igor Kunitsyn 6-3, 4-6, 6-2.