DOHA, Qatar (AP) Caroline Wozniacki swept aside Elena Dementieva 6-1, 6-1 in the group stage of the WTA Championships on Tuesday, putting her one win away from ensuring she will remain the world's top-ranked player for 2010.

Wozniacki of Denmark raced out to a 3-0 lead in the first set on her way to thrashing Dementieva who often had no answer for Wozniacki's strong serves and well-placed groundstrokes.

Very nice start, definitely. I'm very happy to be through this first match,'' said Wozniacki, who had a 4-3 record against Dementieva coming into the tournament.It's always tough to start a new tournament. Against Elena, I knew we have had so many tough matches in the past. It's nice to get this one.''

Wozniacki needs to win two of her matches in the Maroon Group to fend off a challenge for her top ranking from No. 2 Vera Zvonareva of Russia.

The eight-player tournament features the world's top performers in 2010, although the Williams sisters are absent due to injury. The top two players from the two groups will advance to the semifinals.

The humid and hot conditions appeared to influence the outcome of several matches. Temperatures had cooled by the evening from a high of 84 degrees, but players complained about the conditions.

Zvonareva earlier beat a struggling Jelena Jankovic 6-3, 6-0 in the opening match of the White Group. Jankovic said later she became ill during the match, suffering tingling and dizziness.

She told organizers she was too ill to attend a post-match news conference, but would continue in the tournament.

I am still suffering from an illness that affected me last week and I had medical treatment after the match today when I received an IV,'' she said in a statement.I had difficulty breathing during the match, felt dizzy and tingling and felt like I didn't have any power. I finished the match but I had a really hard time.''

Dementieva also blamed the weather for her poor showing, saying the combination of heat and humidity was killing you'' and was the reason she wasgoing for the wrong shots all the time.''

The loss for Jankovic, who held the No. 1 spot in 2008, continues a run of poor form. She has dropped to eighth in the world and was beaten at this month's Kremlin Cup by No. 248 Zarina Diyas. She has struggled for much of the year with injuries - including ankle, back and, more recently, sinus problems.

Zvonareva, meanwhile, has risen to No. 2 in the rankings this year after reaching the finals of Wimbledon and the U.S. Open.

Zvonareva started slowly, but was able to take advantage of several double faults and unforced errors by her Serbian opponent to lead 4-2 and 5-3 in the first set. The Russian closed out the set when Jankovic double-faulted.

Zvonareva said she didn't play her best tennis and made too many unforced errors. But she stepped up her game in the second set and was satisfied to come away with the victory.

Overall, I played really well. Even if I had unforced errors, I was coming up with great shots afterwards,'' she said.It feels amazing to win my first match of the championships.''

She said the difference in the two sets was that she was ``managed to go for my shots and make more shorts without unforced errors.''

In the second set, I found my rhythm and was playing more aggressive and going for my shots and making those,'' she said.I will just have to improve my consistency, maybe little bit better serve and return.''

Also, Samantha Stosur of Australia staged a big comeback from 4-0 down in the first set against Francesca Schiavone of Italy to win 6-4, 6-4 in the Maroon Group.

Using her powerful forehand, the seventh-ranked Stosur was able overcome seven aces from the sixth-ranked Schiavone and her own inconsistent service game.

Schiavone could be seen getting a pep talk from her coach after her struggles in the first set. It seemed to work as she took a 4-3 lead in the second set with an ace. But Stosur stormed back to tie the set at 4-4 with a forehand winner, pumping her fist as the crowd cheered.

The fifth game went back and forth until Schiavone's weak returned was crushed by Stosur to give her a 5-4 lead on her way to the victory.

Stosur said the key to the match was her being able to break Schiavone at 4-0 in the first set.

I think that helped kind of change the momentum a bit,'' she said.Then I held, and then when you start getting a few games back, you never know how your opponent's feeling,'' she said. ``They probably think they should have won the set. So it was just a matter of playing point by point. Then you kind of get into it and things start flowing a little bit more.''