Venus Williams is in little sister Serena's quarter of the U.S. Open draw and if they both win four matches, they will meet in the quarterfinals.

After Serena Williams struggled mostly with herself but won the last match of the day session in Arthur Ashe Stadium Wednesday, Venus followed with a struggle of her own, pushed to three sets by Irina Falconi in the first match of the night session.

Despite making 47 unforced errors over the two-hour and 14-minute match, Venus Williams came away with a 6-3, 7-6 (2), 6-2 win over Falconi that put her into the third round. There she will face the No. 12 seed, Belinda Bencic. Bencic played -- and lost -- her very first WTA match against Williams.

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"The third set I thought I had a lot more clarity," Williams said. "I had the crowd behind me . . . I feel like I'm still playing the important points well."

As Williams, the two-time Open champion, tries to claw her way back to the top tier at the Open at age 35, 21-year-old Eugenie Bouchard is trying to pull herself together after a brilliant season in 2014 that saw her climb to No. 5 in the world rankings. Bouchard has been in free fall this year, her ranking falling to No. 25 with a series of first and second-round defeats. Yet a second-round victory in the Open Wednesday might indicate she's pulled the parachute just in time.

Bouchard toughed out a 6-3, 7-6 (2), 6-3 win over Polona Hercog in a match in the heat of the afternoon on the Grandstand Court. She gets the gritty Dominika Cibulkova next.

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It was a result that gave Bouchard something to be proud of.

"They way I kept my nerve at the end of the third," Bouchard said about the key element to her victory. "This year I've had a couple of matches where it's been tough to close out. I just tried to block that out of my mind, and just keep playing tennis."

It was Bouchard's first match on the Grandstand, which will be demolished after this year's tournament and replaced by a new one that's going up on the southwest side of the tennis center campus.

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"It's the last year of it?" Bouchard remarked. "That's very sad. That's my first time playing on it. It's very intimate. I feel like the people are right there. When I go to the back with my towel, I feel like I could touch someone and they could touch me, which would be really weird. That thought crossed my mind during the match. It's really cool. I really like my experience on Grandstand."

In other matches, the rising Swiss star Bencic was pushed to three sets by Japan's Misaki Doi, 5-7, 7-6 (3), 6-3. Agnieszka Radwanska, the 14th seed, defeated Magda Linette, 6-3, 6-2.