Serena Williams victorious on return to competitive tennis in Miami

(CNN) -- Serena Williams shook off any rustiness after a month-long break from competitive tennis as she launched her quest for a sixth Miami title with a straight sets victory over Italian Flavia Pennetta.

The world No. 1 hasn't played since losing to Victoria Azarenka in the final of the Qatar Open on February 17 but made light work of her unseeded opponent winning 6-1 6-1.

Williams, a 15-time grand slam winner, pulled out of the Dubai Tennis Championships after her defeat in Doha complaining of a back injury but looked in good touch as she raced to victory in just under 80 minutes.

"I think I missed a few shots, but only because I think I was off footwork-wise," she told reporters. "But it's always just good just to win a match and stay in the tournament and keep going.

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"I felt like I should be putting the balls away for my opponent but she was so quick and she was running every ball down."

As for coming into the tournament as the world's best player she said: "It always feels better when you're No. 1. There's nothing like when they announce you and they say, the No. 1 player in the world.

"It definitely gives you a little bit more confidence ... a little more pep in your step. I have a lot of matches to play. If I can just stay relaxed -- I really feel like I can do it, but, you know, I'm sometimes my own worst enemy."

Defending champion and No. 4 seed Agnieszka Radwanska, from Poland, breezed into round three with a 6-3 6-2 victory over Taiwan's Hsieh Su-Wei.

"I was happy to have a quick match," Radwanska was quoted as saying on the WTA Tour's official website. "The first match is always a little bit tough and tricky, especially after Indian Wells, where we had a little bit of different conditions.

"It was a really special tournament for me because I was really playing a lot of good matches against top players and not even losing a set.

"I definitely have great memories from here. And the final was a very good match. Hopefully I can play the same level of tennis this year. I will do everything to hold the trophy again."

China's Li Na, seeded fifth, was also making a return after spending six weeks on the sidelines with an ankle injury but she eased past Dutchwoman Kiki Bertens 6-3 6-1.

"I wasn't nervous before the match today, I was excited," Li told the WTA Tour website. "For the last six or seven weeks I haven't played any tournaments so I was happy to win my first match after such a long time.

"There were a lot of fans there to support me today, I was like, 'Wow!' My game was pretty good today, I followed the plan of what I should do. I just had to believe in myself that I could do it."

Petra Kvitova, the 2011 Wimbledon champion defeated China's Peng Shuai 5-7 6-2 6-2.