Serena William's new year resolution – a Grand Slam clean sweep in 2013

Serena Williams stretches to make a return during her first-round win in Brisbane (Getty Images)

It was a big call, coming so soon after Serena Williams had recovered from surgery. But the former world No 1 believes she can complete a seasonal sweep of Grand Slams for the first time in her career.

Williams began her only tournament warm-up before the Australian Open at the weekend, in technically the opening event of next year's season, even though it is still in the dying embers of a successful 2012 for the American, who won the Olympics, the US Open and Wimbledon.

And after convincingly beating the world No 21 Varvara Lepchenko 6-2, 6-1 in the first round of the Brisbane International, she revealed the two targets on her list: to finish 2012 on a high and to start 2013 in meaningful fashion.

Williams, who has 15 Grand Slam titles to her name, has held all four majors once in her career, when she won the 2003 Australian Open having triumphed in the French Open, Wimbledon and US Open the previous year. But she wants more. She wants to win the Australian Open, which commences in two weeks' time, and do what no woman has done since Steffi Graf in 1988; hold every Grand Slam title in a calendar year.

"I think for me, absolutely," she replied when asked whether the Slam was possible for her for 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."

On her match against Lepchenko – born in Uzbekistan but now a US player – Williams added that she wanted to preserve her 2012 record of losing just four of her 62 matches. "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."

Williams moved freely throughout her match against Lepchenko, easing any fear that she might be hampered by the toe surgery she had undergone earlier this month. She was forced to pull out of an exhibition match in Thailand on Saturday, but revealed she was in no discomfort in Brisbane.

"I was a little nervous, but I was completely fine," she 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."

Eight of the top 10 women are contesting the Brisbane International, with Azarenka and Sharapova receiving byes in the first round. Of the world's top 10, only Agnieszka Radwanska and Li Na are missing. Sixth-seeded Petra Kvitova had a 6-3, 6-4 win over Carla Suarez Navarro of Spain and will next meet Russia's Anastasia Pavlyuchenkova, who beat Lucie Hradecka of the Czech Republic 6-3, 3-6, 6-3.