NEW YORK >> Two points from defeat against Venus Williams at the U.S. Open, Sloane Stephens summoned her best strokes when she needed them the most to reach a Grand Slam final for the first time.

Stephens was so close to defeat before taking the last three games of a back-and-forth semifinal between two Americans at Flushing Meadows, edging seven-time major champion Williams 6-1, 0-6, 7-5 on Thursday night.

“It required a lot of fight, a lot of grit,” said Stephens, who is ranked 83rd after having surgery on her left foot in January and is the fourth unseeded finalist at the tournament in the Open era, which dates to 1968.

At 37, Williams was attempting to become the oldest woman to win a Grand Slam title in the Open era. She was trying to reach her third major final of this season, something she last did 15 years ago. Here’s how long and successful her career has been: Williams’ first title match in New York came in her U.S. Open debut in 1997. Stephens was 4 at the time.

“I’m honestly just honored to be able to play at the same time as her, one of the greatest ever to play our game,” said Stephens, who joined spectators in clapping for Williams when she walked off the court.

Williams was quite near to winning, ahead 5-4 with Stephens serving at 30-all. Two points away. There, they engaged in a 25-stroke point, until Stephens conjured up a backhand passing winner down the line, then wheeled and pumped her fists.

“Venus knows it’s an opportunity lost,” said her coach, David Witt, “because she had it. She had it on her racket.”

At 5-all, Stephens broke with the help of a lob winner that drew a standing ovation from the crowd, and a full-sprint get of a short ball that she turned into a “How did she do that?!” winner at an impossible angle to love 30.

“There was nothing I could do about those shots,” Williams said.

Soon enough, Stephens was serving out the biggest win of her career — and of her impressive comeback from surgery. She returned to the tour at Wimbledon in July, losing in the first round, and lost her next match, too. Her ranking, which reached a high of No. 11 in 2013, dropped out of the top 900.

But since then, Stephens has won 14 of 16 matches.

“I have no words to describe what I’m feeling, what it took to get here,” Stephens said in her on-court interview. “Just the journey.”

On Saturday, Stephens will meet No. 15 Madison Keys or No. 20 CoCo Vandeweghe in the first all-American U.S. Open women’s final since 2002, when Williams and her sister Serena faced each other.

Keys and Vandeweghe were scheduled for the second semifinal later Thursday night. Neither has ever been to a major final.

This was the first time in 36 years that all four women’s semifinalists at the U.S. Open represented the host country, so it was understandable if spectators in Arthur Ashe Stadium were conflicted about which players to pull for.

Williams vs. Stephens was a back-and-forth affair, with a pair of lopsided sets leading up to a classic third. Just when it seemed one woman or the other was in full command, the match would swerve in a new direction.

They both hit the ball hard. They both covered so much ground, Williams getting to seemingly unreachable balls thanks to her long wingspan, Stephens doing the same thanks to her speed.

Fans cheered for Williams when she was shown on the arena’s video boards for a brief pre-match interview in the hallway that leads from the locker rooms to the court entrance. They roared for Williams during introductions after politely applauding Stephens. And they got louder than ever when Williams finally began to work her way back into the match early in the second set.

The far more experienced Williams was shakier in the early going, ceding the initial break to trail 3-1 thanks to four consecutive shots that went awry. The opening set was not much of a contest, thanks mainly to miscue after miscue by Williams — she had 17 unforced errors by the time it was over, 12 more than Stephens.

Williams finished with six double-faults and a total of 51 unforced errors, 24 more than Stephens.

“I just wasn’t playing well. Those are moments where you have to dig deep and figure out how to get the ball on the court and have a big game. I can’t be tentative and try to figure out how to put that ball in,” Williams said. “Clearly she’s seen me play many, many times. I haven’t seen her play as much.”