MELBOURNE -- After her first match, Serena Williams gave herself an A for effort.
Focused from the outset, she showed none of the vulnerability some were expecting after her four-month layoff following last year's US Open.
As for her second-round match? Perhaps an A-plus is in store. Williams beat Su-Wei Hsieh 6-2, 6-1 in exactly one hour Tuesday to reach the third round of the Australian Open.
"I was really focused and, you know, that first round really helped me because I was really just fighting," Williams said. "I really gave a big effort there. Today, again, I just wanted to stay focused for the whole time."
Williams ended the match with a scorching down-the-middle ace, her sixth of the second set.
"She's definitely a tricky opponent," Williams said of Hsieh in her on-court interview. "She was a good matchup for me. She can hit any shot at any time from anywhere in the court. I needed that."
No player -- man or woman -- has more Australian Open titles than Williams' six. Last season, she launched her quest for a rare calendar-year Slam with a championship Down Under. Although Williams fell two matches short in New York, she only added to the numbers that make her the most accomplished player of this generation.
Among her more notable accomplishments:
• Ranked No. 1 for 153 straight weeks
• Oldest No. 1 in history, at 34 years old
• Owns 21 Grand Slam titles, one more than the rest of the field combined
• Has recorded 69 titles
On Wednesday against Hsieh, Williams added to a lesser-known but still impressive stat by upping her record against players who hit with two hands off both wings to 18-2. Among that group of players, only Monica Seles and Marion Bartoli have beaten Williams.
One hand or two, Hsieh was little match for Williams. The Taiwanese player won only seven of 18 first-serve points, or a woeful 39 percent.
With the win, Williams joined Maria Sharapova in the third round. Earlier in the day, with persistent rainfall and the roof on Rod Laver Arena closed for the first time this tournament, the world No. 5 took care of Aliaksandra Sasnovich 6-2, 6-1.
Sharapova thrived under the steadier conditions of the indoor stadium, went full throttle on nearly every groundstroke and finished the match with 22 winners -- nearly four times as many as her opponent. Amid a late-arriving crowd on center court, Sharapova ended the 1 hour, 11 minute affair with a service winner out wide that trickled off the tip of Sasnovich's racket.
"Yeah, I think last year I didn't play an indoor match until the final, so I guess it's good to play in a different environment," Sharapova said. "[I played against somebody] I haven't faced before, which is quite rare, but felt like her game was a little bit unpredictable. I had to make some adjustments. She came up with a few good shots and a few errors, some great big first serves and some shorter ones."
Up-and-coming Belinda Bencic beat Timea Babos 6-3, 6-3. A lot is expected of Bencic, an 18-year-old Swiss who won the Rogers Cup last season. Seeded No. 12, Bencic attacked the net with pinpoint accuracy and won 11 of 13 approaches.
The biggest upset of the day came courtesy of No. 23 Svetlana Kuznetsova, who lost to Kateryna Bondarenko 6-1, 7-5. Kuznetsova entered the Australian Open fresh off a title in Sydney, but the two-time Grand Slam champion was flat from the start. She was broken five times and has now lost before the third round three straight times in Melbourne.
A day after an avalanche of upsets in Melbourne Park -- Venus Williams, Rafael Nadal and Simona Halep lost opening-round matches -- Serena and Sharapova restored some order.
Despite the lopsided score for Sharapova, it wasn't a pristine performance. She faced only two break points in the match against Sasnovich but donated 24 unforced errors.
When asked about her timing, Sharapova said, "Yeah, my toss went off a little bit, but I thought I was able to serve quite well the rest of the match, except that game, so that was good. Improved my returns a little bit today compared to the first match."
As for Williams, she won the first set in just 28 minutes. Plagued by arduous, three-set matches last season, Williams has won all four sets she has played through two rounds in Australia.
Her second match saw a much steadier performance than the one she had in her opener against Camila Giorgi. Against Hsieh, Williams hit 10 more winners than unforced errors.
If the draw plays out according to seedings, Williams and Sharapova will face each other in the quarterfinals.
Last season, the Russian reached the final at the Aussie Open and suffered a straight-sets defeat to Williams. To date, Sharapova has lost 17 straight matches, including three Grand Slam finals, to the world No. 1.