Maria Sharapova stormed into the third round of the Australian Open with a 6-0, 6-1 trouncing of American qualifier Jamie Hampton in glorious sunshine on Thursday.

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The leggy Russian had too much firepower for the 144th-ranked Hampton and wrapped up the match in just 64 minutes at Rod Laver Arena.

Sharapova, who won the 2008 title in Melbourne, the last of her three Grand Slams, sealed the match with an imperious cross-court backhand Hampton could only weakly tap back into the net.

Serena Williams said before the start of the Australian Open that even with just two warm-up matches under her belt she was ready for Melbourne. More than ready it seems.

The American, with lattice-work strapping snaking up from her injured left ankle to behind her knee, brushed aside Czech Barbora Zahlavova Strycova 6-0, 6-4 in just over an hour to reach the third round.

Five-times champion Williams was unable to defend her 2009 and 2010 titles last year due to injury and there were concerns she would not be ready for the year's first Grand Slam after pulling out of the Brisbane International quarter-finals with her sore ankle.

After shaking off the rust in the first round against Tamira Paszek, Williams was on song from the get-go, blasting baseline winners past Strycova and racing through the first set in just 22 minutes.

Her Czech opponent won her first service game of the second set, eliciting enthusiastic applause from the crowd, but the Williams response was predictable, the 30-year-old winning her next serve to love and breaking Strycova to go 3-1 up.

Williams had her first wobble while serving for the match at 5-3, giving Strycova a sniff of hope, and the American looked in trouble when a change of direction left her sitting on the sun-baked court grimacing.

But Williams got back to her feet and promptly broke Strycova's serve to seal the set 6-4 and earn her place in the third round.

When fit, Williams has often been at an elite level of her own over the years and her victory over Strycova was the 500th win of her career.

"It's like the ultimate. It's really, really cool," she said of the milestone, which only her sister Venus, Clijsters and Thai Tamarine Tanasugarn have reached before her among active players.

"Five hundred is a lot of matches to play, let alone to win, so it's pretty cool."

Defending champion Novak Djokovic did just what he needed without being stretched to reach the third round of the Australian Open with a 6-3, 6-2, 6-1 victory over Colombia's Santiago Giraldo.

The 24-year-old Serb, who used last year's Australian Open to catapult him to the world's top ranking and three Grand Slam titles, took a little time to get going in the warm Melbourne sun before he moved through the gears.

Djokovic moved the Colombian around the court with ease, mixed up his pace and angles with several audacious drop shots before the world number one came through in one hour, 42 minutes when Giraldo's backhand sailed long.

French sixth seed Jo-Wilfried Tsonga, a finalist here in 2008, recovered from an early deficit to beat Brazilian Ricardo Mello 7-5 6-4 6-4 and advance to the third round.