Williams pulled out of last week's semi-finals with a knee injury
Serena Williams fought back from a set down to move into the third round of the Dubai Tennis Championship with a 4-6 6-2 6-0 win over Sara Errani.
The world number one lost her first two service games, but finally hit form to sweep through the closing stages.
Her sister Venus enjoyed easier progress with a 6-0 6-1 win over Russia's Anastasia Pavlyuchenkova.
But there was a shock for second seed Dinara Safina as she suffered a 6-4 6-2 defeat by France's Virginie Razzano.
"This was one of my worst performances ever," said Safina. "I just wasn't there. I have been practising well, but sometimes it happens.
"You take time to find your game when you are playing the first match in a new tournament, but I must also add that she played a great match."
Australian Open champion Serena Williams said: "I got off to a slow start, just trying to get used to the conditions, and I did not really like the ball being used here.
"But I never doubted that I will win. Even when I was 4-0 down in the first set, I told myself I am just two breaks down and I can still win the set."
The American added that her knee "held up well" after she pulled out of last week's semi-finals in Paris.
Fourth seed Elena Dementieva beat Sybille Bammer of Austria 7-5 6-2, while Serbian third seed Jelena Jankovic defeated Monica Niculescu 6-3 6-2.
Vera Zvonareva made short work of her match, beating Vera Dushevina 6-0 6-3, and 13th seed Jie Zheng had to come from a set down to beat Australia's Samantha Stosur 3-6 7-5 7-5.
There were also wins for Alize Cornet, Marion Bartoli, Dominika Cibulkova and Daniela Hantuchova.