(CNN) -- Serena Williams and Dinara Safina, the world's top-ranked women's tennis players, made winning starts to their 2010 season at the Sydney Invitational tournament on Tuesday.
No. 1 Williams easily dispatched Maria Jose Martinez Sanchez, beating the Spaniard 6-1 6-2 in the second round after being given a bye.
The American, who was expected to face Justine Henin before the former world No. 1 pulled out of the tournament due to a leg injury, will play qualifier Vera Dushevina in the quarterfinals.
The Russian won 6-3 6-4 against her compatriot Elena Vesnina, who upset eighth seed Vera Zvonareva in the first round.
"It was a good match. It's definitely more match practice," Williams told the WTA Tour's official Web site.
"I'll hopefully get a couple more under my belt. I'm guaranteed at least one more, so hopefully I'll try to win some more. That's the goal."
Second seed Safina had to battle back from a disastrous start before beating world No. 10 Agnieszka Radwanska 7-5 6-4 in her first match since October.
The Russian lost the first five games but managed to save a set-point at 5-4 down and set up a quarterfinal clash with fifth-seeded compatriot Elena Dementieva.
"Well, it was a little bit of a slow start, but it was a start. It was a winning start," Safina said. "It's not easy to play against Agnieszka. She's a top-10 player and plays very smart.
"I was missing my timing until 5-0 but then I found my game. It ended up being a very solid match for me for my first match of the year."
Dementieva progressed with a 6-2 4-6 6-2 win over unseeded Daniela Hantuchova, but her fellow Russian Svetlana Kuznetsova crashed out after losing to another Slovakian, Dominika Cibulkova.
Cibulkova's reward for knocking out the third seed is a last-eight clash with sixth-ranked Victoria Azarenka of Belarus, who beat Japanese veteran Kimiko Date Krumm 6-1 5-7 7-5.
In the men's draw, fifth seed Sam Querrey was eliminated in the first round by unseeded Russian Evgeny Korolev, who won 6-2 5-7 6-4 to set up a clash with another American, Mardy Fish.
Sixth seed Viktor Troicki of Serbia beat France's Florent Serra 7-6 (7-5) 6-4 and will next play former Australian Open finalist Marcus Baghdatis, while German eighth seed will take on France's Richard Gasquet after his 6-3 6-3 win over Juan Ignacio Chela of Argentina.