PARIS—It was well past the beloved lunch hour of the corporate crowd, and this was the penultimate match scheduled for Court Philippe Chatrier. But this venerable old rectangle with red-clay floor was still more than half empty as the French Open’s No. 4 seed, Simona Halep, and Sloane Stephens met in a fourth-round summit.

This was the kind of atmosphere that might lead a diva to fly into a rage and hurl an elegant shoe at someone, or stamp her foot, cross her arms, and refuse to perform. Halep may be many things, but a diva is not one of them. So she just went about her business, inconspicuous as a groundskeeper but driven by her familiar, eager-beaver relish, and swept Stephens out of the tournament, 6-4, 6-3.

“I feel good that I can represent Romania in quarterfinals in this tournament,” were the first words out of an ebullient Halep’s mouth in her press conference. “So it's amazing feeling.”

Like Novak Djokovic, Halep has been drawing motivation as if it were high-voltage electricity from the simple fact that she’s a de facto representative of her homeland.

“It’s something that you should not underestimate if you come from a big country,” her manager, fellow countryman, and French Open champion Virginia Ruzici told me shortly after the match. “At home Romanians see her as a modest person, a humble person. And for this she has become very much loved and famous. The people feel she is a good person, but also with a big heart.”

That big heart was on display, even though it was not overly exercised, in this somewhat flat match. Granted, at No. 19 (seeded No. 15), Stephens is ranked well below Halep, but it wasn’t so long ago that the two were ranked close to each other as Top 20 hopefuls.

Since then, Halep has developed into a player who excels on a week-in/week-out basis, while Stephens seems to struggle on the tour but lifts her game for the Grand Slam events. Halep, 22, reached the first Grand Slam quarterfinal of her career a few months ago at the Australian Open, and until this tournament had advanced to the fourth round of a major only one other time.

Stephens, lover of the big stage, has been to the fourth round or better at a major seven times now. The highlight is a semifinal appearance at the 2013 Australian Open. Rivalry-wise, Stephens had crushed Halep twice on hard courts, while the Romanian won their only previous meeting on clay, back in 2012.

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Eager Beaver

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Those details appeared to level the playing field between two women who presented a striking contrast against a backdrop of tawny clay. Stephens, 18 months younger than Halep, looked chic in a daffodil yellow dress and colorful headband. Her opponent arrived severely sporty in orange-and-blue separates, her skin free of make-up, hair unadorned and bound up tightly into a bun the size of an eight-ball.

This was essentially a match of rallies, in which Stephens got far less advantage out of her superior serve. Her disinterest in taking the net (she went forward six times, three fewer than Halep) suggests that she felt she could beat Halep at her own game. It was an egregious miscalculation.

“Was good for me because I know how to play on clay,” Halep said. “I think I managed very well the match. I opened the angles. I wanted to make her run a lot on court. I think I played aggressive. I dominated the match, I think.”

To which Stephens could only respond, with no great passion: “It was a tough match obviously, but she has played pretty consistent over the last, say, nine months. It's always tough playing someone who is really consistent and has a lot of confidence and just plays a solid game. So it was definitely tough.”

Don’t let those chipmunk cheeks and “just glad to be here” smile of Halep’s fool you. She’s a remorseless ball striker who seems to enjoy nothing more than dialing up the pace of a rally stroke after stroke after stroke until something finally fails and breaks. These days, it’s usually the game or composure of her opponent.

Halep broke Stephens’ first service game and never trailed after the fifth game of the first set. Stephens actually earned one more break point than Halep overall (7 to 6), but one big difference between them today was the intensity and precision of Halep, particularly on big points. She converted every break chance, while Stephens won just four of her seven critical points.

“The thing with Simona,” Ruzici said, “is that even if she has a moment when she makes a bad shot or gets nervous, it’s almost like it gives her more energy for the next point, makes her come more out of herself.”

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Halep came out of herself in a big way after Stephens turned the tables in the first set, breaking her twice to take a 3-2 lead with serve to come. But Stephens played a poor game—all four points she lost were errors, a couple of them ghastly—and allowed Halep to break back.

Stephens had a chance to break back and take a 5-4 lead, but Halep saved the break point with a pinpoint backhand down the line. The American was unable to hold the next game; Halep won it—and the set—with yet another example of perhaps her deadliest shot, the down-the-line backhand.

In some ways, the second set was a carbon copy of the first. But this time it was Stephens who drew first blood with a break and hold that put her up 2-0. But there seemed to be little rhyme or reason in the way she played the next few games, at the end of which a double fault at break point gave Halep a 4-2 lead.

It was Halep’s cue to step things up: She won the next game in a flurry of winners and went on to serve out the match with élan. A player who’s willing to step and dictate to this 5’6” dynamo, who’s fleet as a jackrabbit but feisty as a badger, probably has the best chance of beating Halep. Stephens was not that player on this occasion.

One of the great contrasts between these two women is the way Halep wears her heart on her sleeve, while Stephens keeps her cards close to the vest. Once again, you could just never predict when Stephens would lift her game, or when it would decline. She’s enigmatic, and keeps a tight hold on her emotions. It makes her especially difficult to read.

“I think I feel a lot more than I actually show,” she said. “But when you are out there on the court and you're showing a lot of emotions and showing this and that, that is definitely something your opponent feeds off of. I just try to keep it inside and play my game and focus on myself rather than get too caught up in the emotions.”

That confirmation was welcome on a day when Stephens’ greatest ability may have been that ability to keep whatever she was feeling deep within. Deep enough, perhaps, to do more harm than good.