BRISBANE, Australia (AP) -- Serena Williams joked that since the calendar still read 2012, she needed to maintain this year's dominant form.
The 15-time Grand Slam champion opened her 2013 season Sunday, and Williams needed less than an hour to beat fellow American Varvara Lepchenko 6-2, 6-1 in the first round of the Brisbane International.
Williams won 31 of her last 32 matches during the 2012 season, including titles at Wimbledon, the Olympics, the U.S. Open and the WTA Championships. She was 58-4 overall.
"Tomorrow is the last day of the year, so technically I still had my 2012 rep on the line," she said. "I really needed to win today so I could finish the year with still just the four losses. So that was important for me."
The third-ranked Williams didn't show any signs of the minor surgery on her big toes that forced her to withdraw from an exhibition in Thailand. She moved freely throughout the match against the 21st-ranked Lepchenko.
Williams saved five break points in the first game as she adjusted to a strong breeze.
"I was a little nervous, but I was completely fine," Williams said. "The doctor said I would be fine. I was excited to get an early start, so just in case I did have any pain, I could have tomorrow off. But everything was fine."
Williams said she didn't believe in New Year's resolutions. Goals are a different story, and she's aiming to sweep the major tournaments.
She held all four Grand Slam championships at one point, winning the 2003 Australian Open after claiming the French, Wimbledon and U.S. Open titles in 2002. But she's never completed a season slam.
"I think for me, absolutely," she said of whether it was possible in 2013. "I think maybe whoever wins the Australian Open will have that same thought. I think there is no way that Victoria (Azarenka) or Maria (Sharapova) or maybe some other players don't feel the same way. So I think I definitely feel that way."
And if that doesn't happen, she plans to give herself a few more years to attempt it. Her experience at the London Olympics made her want to keep playing until the 2016 Games in Rio.
Eight of the top 10 women are entered in the Brisbane International, with Azarenka and Sharapova getting byes in the first round.
Sixth-seeded Petra Kvitova beat Carla Suarez Navarro of Spain 6-3, 6-4 and will next meet Russia's Anastasia Pavlyuchenkova, who beat Lucie Hradecka of the Czech Republic 6-3, 3-6, 6-3.
In other matches, Australian wild card Jarmila Gajdosova beat 16th-ranked Roberta Vinci 4-6, 6-1, 6-3 to set up a second-round match against Sharapova. Urszula Radwanska of Poland beat Tamira Paszek of Austria 2-6, 6-0, 6-2, and Slovakia's Daniela Hantuchova had a 7-5, 6-2 win over Lourdes Dominguez Lino of Spain.
Australia's Samantha Stosur was headlining the night session Monday.