Serena Williams, right, defeats Venus in three sets to keep alive her quest for a calendar year Grand Slam. (Adrees Latif/Reuters)

As if a meeting between Serena and Venus Williams with a Grand Slam at stake wasn’t a stagy enough drama, there was Oprah’s entrance for added emphasis. The TV cameras treated her arrival at the U.S. Open like an awards show red carpet. Then there was Dr. Oz, and Nas, and Donald Trump’s hair, all of them upstaged by a champion performance under the high pressure and brilliant tungsten lights of Arthur Ashe Stadium.

The U.S. Open can sometimes try too hard to be a Broadway-style “event,” and between the tense moments, there was a certain distracting sideshow silliness to this quarterfinal match Tuesday evening, what with John McEnroe swapping bro handshakes with Trump in his luxury box to boos, and beauty shots of actors Candice Bergen and Alan Cumming on the big screens. The combination of buzz and stress might have undone Serena in her quest to become the first woman in 27 years to complete a calendar sweep of the Grand Slams, and that was to say nothing of the coercive pressure her older sister put on her, with her javelin-like strokes. It was fair to say there was no such thing as an unforced error in this peculiar match, won by Serena in three sets of wildly diverging quality, 6-2, 1-6, 6-3.

“Down to the last point, it wasn’t easy,” Serena said.

But fittingly, it ended with a purely sincere and unforced gesture, when the two siblings met at the net. As Serena met her with a grimace, Venus Williams put one arm around her younger and better sister, and then she put another arm around her, for a full familial embrace. It brought the largest applause of the night from the sellout crowd of 23,771.

“It’s a really great moment,” Serena said. “She’s the toughest player I ever played in my life, and the best person I know.”

How to find the right emotional stance from which to play a sister, doubles partner and lifelong roommate? Serena said frankly after advancing to the quarters that Venus was “the only player in the draw I don’t want to play. And not only because she’s my sister.”

It was because Venus was a seven-time winner of Grand Slam titles who knew her every mental and physical habit, “she knows how to beat me and knows my weaknesses better than anyone.” They had trained together daily since they were small children, and share a home together.

A match like this was the end game, the final prize, why they had surrendered their childhoods to the game. “We trained all our lives to be on this court,” Serena said afterward. They began playing tennis in public at the ages of 8 and 10, respectively, trumpeted by their father Richard as “Cinderellas of the ghetto,” prodigies from Compton, Calif., hitting with dead balls on a cracked court. Shortly after Venus won the Southern California girls’ 12-and-under title at age 10, Richard used her promise to move the family to Florida so Venus and Serena could train on scholarship with Rick Macci, who had tutored Jennifer Capriati and Mary Pierce.

They were leggy, spring-loaded kids who hit out on every shot, unafraid to spray errors into the backstop in their efforts to beat the ball deep. Venus was the more willowy and mature player initially at 6 feet 1, but with the milder voice and temperament. Serena glowered at being smaller, and overlooked, which may explain the furious thrust of her game. Both grew into the purest power players the women’s game has ever seen.

“She’s fast; I’m fast,” Serena said earlier in the week. “She hits hard; I hit hard. She serves big; I serve big.”

Their sister act has captivated the public ever since Venus formally turned pro in 1994 at the age of 14. They first met in a Grand Slam tournament match in 1998, when Serena was still just 17. From that point on, they see-sawed for dominance of the women’s game, until Venus was stricken with Sjogren’s disease, an auto-immune ailment, in 2011. This was just the second time in six years they had met in a Grand Slam, and in the meantime, Serena has surged ahead, now holding a 16-11 edge in their 27 meetings.

If there was an emotional toll to the rivalry, any buried resentments or family psychodramas, they were not inclined to admit it publicly.

“I feel like that’s what we always wanted growing up: just to be out there on the big stage duking it out when someone named Williams will win,” Venus said.

But their parents, Richard and Oracene, long ago announced that they couldn’t bear to watch when the sisters had to play each other.

Earlier in the week, Serena said frankly that she deals with any psychological vulnerability on the court by treating her sister as an “enemy,” just another faceless opponent. That attitude was in evidence when she won the final game of the first set. They had traded massive slugging strokes, forcing each other off-balance, for much of it. “She came out hitting so hard,” Serena said. But the auto-immune disease means that Venus suffers from fatigue and joint pain, and has lost her speed and agility through lack of training. Serena exploited that lack of mobility to create set point, with a ruthless drop shot followed by a lob.

“Losing isn’t fun,” Venus said. “. . . But I’m still very excited to see Serena have a chance to win the four majors.”

For more by Sally Jenkins, visit washingtonpost.com/jenkins.