Serena Williams eased into the third round of the WTA Dubai Open in her first match since injuring her back at the Australian Open.

The world No.1 downed Ekaterina Makarova 7-6 (10-8) 6-0 on Tuesday.

The 32-year-old American had a decent tussle in the first set having to save two set points against the world No.24 from Russia before settling into her groove to romp through the second set.

Williams, who took a last moment wild card into this tournament, began gingerly and took about an hour before she hit the ball with anything like her usual authority.

Once she started to do that, she prevailed quickly, finishing the match feeling more hopeful that it might have been the right decision to compete again for the first time in four weeks.

“It was really difficult at first and I was a little bit frustrated,” Williams said.

“I was making a lot of errors I don’t usually make, and my serve was not popping. But I stayed positive, and the second set was better. The body felt all right.”

Williams has a day off during which she will learn whether she next plays Jelena Jankovic, the former world No.1 from Serbia who criticised the legend’s behaviour after losing to her in the final of the WTA (season-end) Championships, or Lucie Safarova, the in-form world No.28 from the Czech republic.

Williams earlier described the injury which had prevented her from making her scheduled return to the tour last week in Doha as “just really rib issues.”

Earlier her elder sister Venus Williams learned that her second round opponent will be Ana Ivanovic, the former world No.1 from Serbia, who saved a match point to survive 3-6 6-3 7-6 (8-6) against Angelique Kerber, the sixth seeded German.