Maria Sharapova and Li Na crushed hapless opponents Monday to storm into the Australian Open second round, making their intentions clear as they bid for further Grand Slam glory.

Fellow major winner Venus Williams also romped on a warm Melbourne Park day, but fourth seed Agnieszka Radwanska was put through her paces by local qualifier Bojana Bobusic before finding her groove.

World number one and defending champion Victoria Azarenka, and tournament favourite Serena Williams, looking for a sixth Australian crown, play on Tuesday.

Reigning French Open champion Sharapova, who was hammered by Azarenka in last year's Melbourne final, was at her dominant best against fellow Russian Olga Puchkova on Rod Laver Arena, humiliating her in a rare double bagel.

Sharapova, the champion in 2008, powered through 6-0, 6-0 in just 55 minutes and will next play either Croat Petra Martic or Misaki Doi of Japan.

China's world number six Li, the runner-up two years ago, overpowered Kazak Sesil Karatantcheva 6-1, 6-3 while seven-time Grand Slam winner Venus, watched by sister Serena, eased past another Kazak Galina Voskoboeva 6-1, 6-0.

Radwanska, who won lead-up events in Auckland and Sydney, was pushed hard by Bobusic in the first set before winning 7-5, 6-0. Ninth seed Samatha Stosur also secured her passage into the second round.

Second seed Sharapova came into the season's opening Grand Slam without any competitive matches under her belt after a collarbone injury ruled her out of the Brisbane International, but showed no evidence of the problem on court.

"I didn't want to focus on the fact I hadn't played a lot of matches, just wanted to focus on what was ahead of me and really concentrate and be aggressive," said the Russian, who has won four Grand Slams.

"I also never faced her before. So it was just one of those matches where I didn't try to worry about her too much. I just tried to think about what I had to do."

Wearing a summery yellow dress and matching shoelaces, the 25-year-old won her opening serve then broke her 107th ranked opponent to take a 2-0 lead.

Grunting at full volume, she used her powerful forehand to devastating effect. Puchkova had little answer to the Sharapova weaponry and pushed a backhand long to cap a humiliating defeat.

Playing in her 10th campaign at Melbourne Park, Sharapova is looking to avenge the humbling she was dealt by Azarenka in the final last year, when she was thrashed 6-3, 6-0 in just 82 minutes.

Li, who complained of tiredness in the lead-up to Melbourne, was also in fine form to set up a second round clash with Olga Govortsova of Belarus.

The 2011 French Open winner seized control by breaking for 3-1 and then 5-1 to take the opening set with ease. Karatantcheva made her work harder for the second set but her resistance ultimately proved futile.

"It's always tough in the first round. You just come to the court 50/50. You never know whether you can beat her or you can lose. Everyone is the same," said Li.

Venus Williams has dropped down the rankings and is only seeded 25 here as she works her way back after illness.

She has not won a Grand Slam singles title since her 2008 success at Wimbledon, but looked in ominous touch against Voskoboeva.

"I don't think my opponent quite got the hang of it. It's hard to play the first match in a major, first thing of the year, and that can be a lot of pressure," she said. "I did my best to just close it out."

It set her up for a second round clash with either France's Alize Cornet or New Zealand's Marina Erakovic, and a potential third round showdown with Sharapova.