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 today.
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 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. Fifth seed Angelique Kerber and ninth seed Samantha Stosur also secured their passage.