Serena Williams moved to within two wins of becoming world number one for the first time in two-and-a-half years after reaching the third round of the Qatar Open here on Tuesday.

The Wimbledon, US Open and Olympic champion showed no obvious signs of physical discomfort during a 6-2,6-1 win over Daria Gavrilova, the 18-year-old former world number one junior from Russia who had reached the main draw as a lucky loser.

This may be some comfort for Williams after finishing last month's Australian Open with an upsetting quarter-final defeat and back and ankle injuries.

However Williams played well within herself, stroking the ball smoothly, and avoiding stressful movement as she concentrated on making efficient progress without mishap.

"I am very happy to be here," said Williams, which was undoubtedly true given the size of her damaged ankle three weeks ago, and the extent of her disappointment at not reaching world number one in Melbourne.

"I feel really good. I played a really tough girl who has been junior champion, so I think it was a really good match."

Some of those words sounded like diplomatic niceties, because from 2-2 onwards Gavrilova was outclassed and Williams took nine games in a row at a canter in the middle of the match.

She completed the task in less than an hour, and that was without her fearsome first serve - which had a low accuracy rate 52 percent - really functioning as her best weapon at all.

Williams was also a little shaky at the end, and became annoyed with herself for a few mistakes. She had however done the main task, which was to show that she may be fit enough still to have a decent chance of becoming world number one again.

Williams said that her ankle was behaving itself.

"It held up good. I have it heavily taped. As long as the tape doesn't get loose, it feels really good."

"I think mostly how I have been playing is just trying to play smooth and avoid problems."

Her next opponent is the winner between Roberta Vinci, the 15th seeded Italian, and Urszula Radwanska, the world number 37 from Poland.

If Williams fails to reach the semi-finals Maria Sharapova has a chance of regaining the number one ranking, and the French Open champion began with a 6-3, 6-2 win over French qualifier Caroline Garcia.

Sharapova started like a train, winning eight of the first ten points, and breaking serve twice before Garcia could find a way of sometimes escaping from her penetrating drives.

"I was quite happy with the way I played, because, you know, my opponent has already played a few matches here, and been able to get into the match atmosphere," said Sharapova.

"So I wanted to start really strong. I also had a tough match in my previous encounter against her, where we played three sets. I really wanted to start better this time."

Sharapova will next play the winner of Klara Zakapolova, the world number 24 from the Czech republic, and Sloane Stephens of the United States.

Stephens, who reached the semi-finals of the Australian Open with a sensational win over Serena Williams last month, came through with a 6-2, 6-2 win over Anna Tatishvili, the world number 57 from Georgia.

It was an especially convincing performance given that she had been ill after her Melbourne heroics, and also had to adapt for the first time in her career to the pressures of celebrity.

"Of course I had people tweeting me and stuff, "Stephens said". And I wanted to make time for like my friends and see like the people who I was supposed to see.

"So, I mean, it was just really tough the first week (after the Australian Open, but then I was glad that I was able to just stay home.

"I mean, I got sick, which was unfortunate, but other than that, it was I mean, the first week was tough, but I adapted well, I think."

Source: AFP