NEW YORK—“Payback time, Serena,” someone called from high in the stands in Arthur Ashe Stadium as Serena Williams took the court against Sloane Stephens on Sunday. The theme of this tense afternoon had been stated, and it would run through their match from start to finish.

Still, Stephens, who had beaten Williams at the Australian Open early this year, didn’t appear intimidated by the moment, at least not at first. For a set and a half, she stood toe to toe with Serena, as the two women gave us the most intense tennis of the women’s Open so far. Serena’s serve was sharp to start, and she played with controlled aggression all afternoon. She struck the ball cleanly and was rarely off-balance, the way she can be when she’s struggling. Williams finished with 22 winners against 13 errors, and there were few signs of the nerves that she has fought on some other big occasions recently. Serena’s only hiccup came when she was serving at 4-2 in the first set, when she double-faulted twice and was broken. On the whole, this was Serena at her most dialed in and determined, the woman who rises to the pressure occasion.

For her part, Sloane is one of the few players who can match Serena’s pace and make her play defense on a regular basis. Stephens rifled forehand winners that thrilled the crowd, which was mostly behind her. When she had time to set up for that shot, she went for it and was lethal with it. In the first set, when she was able to match Serena’s intensity and shot-making, you got an idea of just good Sloane could be.

In the end, though, Sloane’s offensive firepower only highlighted how underrated Serena’s defense is. Few players make Serena scramble the way Sloane did today, but scramble she did. She forced Stephens to hit one more ball to finish rallies, and she returned serves that would have been aces against almost anyone else. The effort needed to win points eventually caught up with Sloane, who lost her early intensity in the second set and finished with 29 errors. For all of the bullets she hit, she only finished with 15 winners, a testament to Serena’s court coverage.

Sloane also struggled to make a dent on Serena’s serve, earning just two break points for the match. The last came in the opening game of the second set. Serena looked tight and off-balance in that game, and a momentum swing appeared possible. But she settled down quickly and saved the break point with a well-constructed crosscourt/down-theline forehand combination. The moment to panic had come, and Serena hadn’t panicked.

After a 52-minute first set that was filled with multi-deuce games, the end came rapidly in the second. Up a game point at 1-2, Sloane double faulted. At break point, Serena again frustrated Stephens with excellent defense. When Sloane fired a forehand into the net to make it 3-1, Serena didn’t look back. In full control, she raced through a 35-minute second set over a slump-shouldered Sloane for a 6-4, 6-1 win.

Serena moves on to face Carla Suarez Navarro in the quarters. Afterward, Serena praised Sloane and talked up the bright future of American tennis that she represents. It was, perhaps, left to her sister, Venus, to provide the true family reaction. All through the last game, as Serena drove the final nails into the coffin with 120-M.P.H.. serves, Venus sat in the player's box with a thin but unmistakably satisfied smile across her face. It was a payback kind of smile.

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U.S. Open: S. Williams d. Stephens

U.S. Open: S. Williams d. Stephens

IBM Stat of the Match: Serena won more than 50 percent more points than Stephens (75 to 49), a result of the younger American's 29 unforced errors.

IBM is a proud sponsor and official technology partner of the U.S. Open. For more information on this match, visit IBM's SlamTracker.