NEW YORK (CBSNewYork/AP) — Two-time champion Venus Williams won a place in the third round of the US Open Wednesday night for the first time since 2010, a year before she announced she had been diagnosed with an autoimmune disease.

The 19th-seeded Williams, at 34 the oldest woman left in the draw, did not need to deal with too much trouble while beating 78th-ranked Timea Bacsinszky of Switzerland 6-1, 6-4 Wednesday night.

Well, now I’m happy. I won a match again. Finally I did something I couldn’t do the last couple years,” Williams said. “That’s good stuff.”

She showed bits and pieces of the type of game that once lifted her to the top of the sport — the No. 1 ranking and seven Grand Slam singles titles, including at Flushing Meadows in 2000 and 2001.

Against Bacsinszky, Williams saved all four break points she faced, converted 3 of 11 she earned, and avoided too many unforced errors, finishing with 12 fewer than her opponent.

“I feel like I’m playing well. I feel like I play my best when my opponent pushes me, really. Once we really start to get into a slugfest, I feel like I really relax. Sometimes I feel like when they aren’t pushing me as much, maybe I’m a little too passive at times,” Williams said, rolling her eyes at that last thought.

“But I do feel — like I can rely on myself to compete really well,” she continued. “So that’s a good feeling.”

For a spot in the fourth round, she will need to get past Italy’s Sara Errani, who was the runner-up at the 2012 French Open and also reached the U.S. Open semifinals that year.

Looking ahead to her matchup against Williams, Errani said: “I’ll definitely have to raise my level of play and hit deep, try to make her move.”

As recently as 2010, Williams made it all the way to the semifinals at the U.S. Open.

But in 2011, she withdrew from the hard-court tournament before she was supposed to play Sabine Lisicki in the second round, saying she had Sjogren’s syndrome, a condition that can cause joint pain and sap energy.

Williams then lost second-round matches in New York to Angelique Kerber in 2012, and to Zheng Jie last year.

“The last couple years, I fought really hard and I really played red-hot opponents. So it wasn’t like I didn’t try. My opponents, they played so well. Sometimes you don’t win `em,” Williams said.

“That’s why you get up and you live to fight another day,” Williams said. “So that’s really what it’s about for me.”

Also in women’s singles, Italy’s Sara Errani topped Russian-born Australian Anastasia Rodionova 6-4, 7-6.

Meanwhile Wednesday, brothers Bob and Mike Bryan opened their quest for a fifth U.S. Open crown and their 100th overall title together with a 6-2, 6-3 first-round victory in Men’s Doubles over Max Mirnyi and Mikhail Youzhny.

The 36-year-old Bryan twins, the world’s top-ranked doubles team, slammed six aces and never lost serve in an efficient victory that got them off court in less than an hour.

While the Bryans have won a record 15 Grand Slam tournament doubles titles, they have not taken one since Wimbledon 2013, a drought they attribute to the thin margins of the doubles game that leave no clear favorite and 15 to 20 teams that could potentially win the tournament.

“Holding serve is so big and returns have to be so precise,” Bob Bryan said.

Mike Bryan added they are hitting their stride after taking their 99th career title earlier this month in Cincinnati: “We’re feeling good and we’re healthy and we’re going to put ourselves in position to win another one of these, if not this week, then soon.”

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