NEW YORK — Venus Williams figures matches against her sister would be much less stressful if they weren’t both elite players.

“If I had a sister and she wasn’t very good, then it would be just not really a big deal because I would beat her,” she said Monday at the U.S. Open, after she and Serena assured a quarterfinal showdown.

But Serena wouldn’t change anything about their tennis prowess.

“I’m glad we’re both pretty good at it, because I always use her,” she said. “If I’m going somewhere and they give me a nice gift I’m like, ‘Well, my sister, she’s not here, but she would love that.’ If she was no good then I wouldn’t be able to do that. And I always keep it. She doesn’t even know about it half the time.

“I guess maybe she’ll know about it now.”

Both sisters easily won their fourth-round matches to set up their 17th meeting as pros. Venus, seeded seventh, beat No. 9 Agnieszka Radwanska of Poland 6-1, 6-3. No. 4 Serena defeated wild-card entrant Severine Bremond of France 6-2, 6-2.

The winner will earn bragging rights — at least temporarily. Each has won eight times in the all-Williams tilts. That includes 10 matchups at major tournaments, with each posting five victories.

The two would prefer to meet later than the quarterfinals, just as they did at Wimbledon, when Venus prevailed in the final. Considering how well both are playing right now, it’s not hard to envision that this match could determine who goes on to win the Open.

“I definitely think it’s possible, but this is only the quarterfinal,” Serena said. “So, you know, whoever wins this will be going on to the semis and fighting.”

Wednesday will mark the first time since 2003 that they’ve squared off at consecutive Grand Slam tournaments. “Classic” and “unique” are the words Serena used to describe their matchups.

What about “difficult?”

“No, not anymore,” she said. “No. Just another match, another possibility for me.”

Also advancing Monday were No. 6 Dinara Safina, who defeated Anna-Lena Groenefeld 7-5, 6-0, and No. 16 Flavia Pennetta, who beat No. 32 Amelie Mauresmo 6-3, 6-0.

In men’s action, No. 1 Rafael Nadal held off 55th-ranked Sam Querrey, a 20-year-old Californian who never before had been to the fourth round at a major tournament. Querrey hung in during extended baseline rallies, and briefly led in the third set, before losing 6-2, 5-7, 7-6 (2), 6-3.

Nadal owns four titles from the French Open and one from Wimbledon, but he’s never been as far as the U.S. Open semifinals. He’ll try to take care of that when he meets another unseeded American, Mardy Fish, in the quarterfinals.

Also advancing was No. 17 Juan Martin del Potro of Argentina, who ended the run of Kei Nishikori, the first Japanese man to reach the U.S. Open’s fourth round in the 40-year Open era. Del Potro won the contest between teenagers 6-3, 6-4, 6-3 for his 23rd consecutive victory.

Del Potro will face No. 6 Andy Murray, who beat 10th-seeded Stanislas Wawrinka 6-1, 6-3, 6-3. Tempers flared when the two played in Rome in May.

Murray claimed del Potro insulted his mother during a first-round match. Judy Murray provided vocal support for her son from the stands.

Del Potro nearly hit Murray in the head with a ball in the second set. The Argentine retired while trailing 5-7, 6-4, 1-0.

Murray was asked Monday if he was surprised del Potro hadn’t tried to clear the air.

“I’ve known him since we were really young,” Murray said. “Doesn’t really bother me. I wasn’t great friends with him before. I don’t need to be friends with him now.

“So, no, I’m not surprised.”

Fish serve-and-volleyed his way past No. 32 Gael Monfils in straight sets. As for facing Nadal?

“I feel like a guy with my style of play is someone that he doesn’t want to see,” said Fish, who won the point on 45 of 69 trips to the net. “You’ve got to be able to finish points quickly. He’s going to last longer than anybody. He wants to keep the points as long as possible and run the guys down, kind of body-blow after body-blow.”

Nadal, who’s won 42 of his past 43 matches, had to work hard to wear down the 6-foot-6 Querrey. When Nadal served for a two-set lead, Querrey broke him at love. When Nadal was trying to put the kid away, serving with a 4-2 edge in the fourth set, Querrey compiled seven break points.

“The match was crazy like that, no?” Nadal said.

He saved each of those seven break points, though, and that pretty much was that.

“He had to earn it,” Querrey noted proudly. “I didn’t just give it to him.”

Venus Williams faced what should have been an opponent to be taken seriously: Not only is Radwanska ranked in the top 10, but she won her only previous match against the elder Williams sister and upset then-defending champion Maria Sharapova at last year’s U.S. Open.

Radwanska needed 27 minutes just to claim a game this time and never came up with a reply for Venus’ constant forays forward. Venus won the point 25 of 34 times at the net, and she put together a remarkable 33-11 advantage in winners.

“She was playing very aggressively, going to the net all the time. There was nothing I could do,” Radwanska said. “She was too good.”