NEW YORK (Reuters) - Serena Williams gained a measure of revenge and a place in the fourth round of the U.S. Open on Saturday as she beat Ekaterina Makarova of Russia 6-4 6-0 in a tougher encounter than the scoreline suggests.

Serena Williams of the U.S. hits a return to Ekaterina Makarova of Russia during their women's singles match at the U.S. Open tennis tournament in New York September 1, 2012. REUTERS/Jessica Rinaldi

Makarova beat Williams at the Australian Open in January but the Wimbledon and Olympic champion turned the tables and needed one hour, 21 minutes to advance to the last 16 at Flushing Meadows.

"I felt like I played better today," Williams told the crowd inside Arthur Ashe Stadium.

"I played such a good opponent - she beat me at the Australian Open so I knew going into today I needed to play better and I definitely felt like I played a little better."

In scorching conditions, the left-handed Makarova gave three-time champion Williams plenty of trouble and hung in well in the face of some heavy hitting from the American.

The first four games alone lasted 20 minutes but eventually Makarova buckled under the pressure and Williams gained the crucial break in the 10th game to take the set.

"I was trying to get that break the whole time - but (at the end of the second set) I started playing a little better and a little more consistent," she said.

An early break in the second set broke the resistance of the world number 42 and Williams, who hit eight aces and 31 winners, eased to victory.

The fourth seed now plays either another Russian, the 14th seed Maria Kirilenko, or Andrea Hlavackova of the Czech Republic.

Williams turns 31 later in September but said she had no intention of following Andy Roddick and Kim Clijsters into retirement.

"I am nowhere near close to retiring," she said. "Now that Andy and Kim are gone I feel like I have to stay out here. I'm not going anywhere."

(Editing by Steve Ginsburg)

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