Sloane Stephens beat Madison Keys, 6-3, 6-0, in the U.S. Open final to win her first career grand slam. (Adam Hunger/Associated Press)

Sloane Stephens, the 24-year-old American who made a splash at the 2013 Australian Open, saw it turn to ripples and then smaller ripples and then the silence of an 11-month absence, completed a mind-boggling five-week rise Saturday. She became a U.S. Open champion when she played her first Grand Slam final as if it were her 10th: with a steadiness that verged on airtightness.

As Stephens combed her way through her 6-3, 6-0 win over fellow American and dear friend Madison Keys in Arthur Ashe Stadium, it became a game within the game just to observe a single statistic: unforced errors. Midway through the second set, Stephens had three, Keys 25. The numbers ended on six and 30, and they demonstrated how Stephens ignored the circumstances to access her utmost form of demanding defense, while Keys couldn’t do the same to pursue her customary attack.

“There’s no word to describe how I got here,” Stephens said.

In fact, it seemed as if she must have dwelled in some rare, big-time-athlete zone, remarkable for a debutant. Told she had committed a puny six unforced errors, she blurted, “I made six unforced errors in the whole match?”

Told yes, she said, “Shut the front door! I don’t think that ever happened to me before. Oh my god. That’s a stat. Snaps for me.” She said, “I just went out to compete and ran after every ball.”

Thereby did the U.S. Open title go to a woman who forced Keys’s nerves to fray exponentially with the deathless groundstrokes that came from Stephens’s compelling aplomb, as well as a woman who reached August ranked 957th.

That ranking, of course, lay well beneath Stephens’s long-established quality, even if that quality had not led her back to any Grand Slam semifinal after her burst past Serena Williams to the 2013 Australian Open final four and had seen her go 13 Grand Slams since 2014 either reaching only one fourth round or absent altogether. It owed to her 11-month absence for foot surgery, during which she spent the Australian Open on the couch in a cast. That left her grateful just to play again and to play at Wimbledon, at which she lost to Alison Riske in the first round, an outcome she repeated in Washington against second-ranked Simona Halep on the night of Aug. 1, a mere 39 days before Saturday.

“You could look at that as a bad draw, right?” said Kamau Murray, Stephens’s coach the past two years. “But we always talked about, ‘You’ve got to earn your way back on this.’ We didn’t get some of the wild cards [into tournaments] that we expected to get on her comeback, and so, ‘This is a sign. You’re going to have to earn your way back on this tour.’

“That means, ‘You didn’t get the wild card here and there. You’ve got Halep in the first round here.’ You know, it was like, ‘Well, let’s just earn it.’ Let’s not cry for spilled milk. Use your protected ranking if you have to and just go play. So I really was just using it as a measuring stick for a level of competitiveness, right? And if you look back at that match, she had a set point in the first set, and then she lost the second set 6-0. So we just said, ‘Okay, the level of the competitiveness is there. We just need to be able to sustain it.’ And that, of course, comes with time.”

It came with 39 days.

She proceeded to Toronto ranked 934th. “I was literally horrified I wasn’t going to be able to get into a lot of tournaments,” she said. From there, though, Stephens climbed and then climbed dizzyingly. She got to the semifinals in both Toronto and Cincinnati, and by the time she got done Saturday, she had won a whopping 15 matches in three tournaments in five weeks this summer, all against top 50 players, five against top 10 players and nine against top 20 players.

“I went from super-excited to be on the court to super-excited I was playing well to super-excited I just won the U.S. Open,” she said. Asked in a rollicking news conference whether the title had fed her hunger for another, she wisecracked, “Of course, girl. Did you see that check [$3.7 million] that lady handed me? Man, if that doesn’t make you want to play tennis, I don’t know what will. Man.”

It all did seem dreamlike, unreal.

“When I had surgery, I was not thinking that I would be anywhere near a U.S. Open title,” she said. “Nor did I think I was going to be anywhere near the top 100. I was worried about my protected ranking [the provision used for injured players], and I was worried about using my protected ranking to get in here.” Now, she said in the odd language of tennis, “my ranking is higher than my protected ranking.”

Come Monday, she will hold down a ranking projected at No. 17.

The points packed so quickly into that ranking included those claimed through a stirring three-set survival of Venus Williams in the semifinals, 7-5 in the third, and then the quick push through Keys, which ended in a mere 61 minutes on a third match point.

“Sloane’s a tough opponent to play when you’re not making a lot of balls, but then at the same time, she’s not going to miss, either,” Keys said. “So it was kind of, I didn’t totally know what to do once I got on the court, which just intensifies those nerves even more.”

So as one last Keys error slammed into the net after a booming final game, Stephens turned to her family and team up in the stands and put her hands on her hips, as if startled. “Just like, wow,” she said later. “How insane. I actually won the U.S. Open.”

She then engaged Keys, her chum in this final between two dear friends, in perhaps the longest post-match hug tennis has seen. In the front row beamed Stephens’s mother, Sybil Smith, an American athletic pioneer who swam for Boston University and became the first African American, all-American swimmer, finishing sixth in the country in the backstroke.

From there, Smith exited to the concourse, stopping briefly for well-wishes and selfies and thanking the strangers who said something neither she nor her daughter would have expected merely five weeks ago: “Congratulations, Mom!”