Watching Serena Williams score her fifth US Open women’s singles title last evening, I couldn’t stop thinking of Billie Jean King’s advice on winning. During the first two sets of Sunday’s nearly three-hour thriller vs. Victoria Azarenka, Williams could hardly get out of her own way, committing double faults and unforced errors as nasty wind gusts visibly rattled her.

How does a champion adjust—and pull out the victory? Here’s wisdom that King, who won the women’s singles title at the US Open four times 40 years ago, shared in an interview that I did with her in June at Fortune’s Most Powerful Women conference in London. King’s advice is as applicable to business–and life–as it is to tennis:

1. Own your feelings. “Everybody chokes. The most important thing that I learned is to admit what’s going on.” At one critical moment at Wimbledon decades ago, King was serving at game point in front of the Royal box. “My hands were shaking. My knees were knocking. Finally, I said to myself, ‘I am so nervous. I’m about ready to throw up.’ As soon as I said that, I was fine–because it defused it. It’s like saying, ‘I have a problem.’ You have to take ownership of your feelings. I did, and I won the point. It was huge.”

2. Stay in the solution. “In a match, 75% of the time, you’re not hitting a tennis ball. The champions use that 75% better than anybody else. And they’re stronger emotionally. Emotionally, not mentally. Everyone says, ‘Oh, they’re mentally tough.’ Mental is what you think; emotional is what you feel. Most of us break down when we get nervous, because of what we’re feeling. You have to stay in the solution. When you commit an error, you take in the information. I call it, not failure. I call it feedback. When we fail, it’s really feedback.”

3. Know why you win. “I try to get people to concentrate on why they win. I’ll ask a young person when they come off the court, ‘Why did you win?’ I’ll spend a lot more time on that than why they lost because it starts to build up the self-confidence that you need to understand your strengths. If I can get someone to understand why they win and what makes them tick, their chances of winning are so much greater.”

Williams’ 7-5, 6-7, 6-1 win against No. 2 seed Azarenka marks her 17th Grand Slam singles title. At age 31, she is one championship shy of the 18 won by Martina Navratilova and Chris Evert. In the history of women’s tennis, King says, “Serena’s the greatest player ever.”

As for King, she’s earned her title as “the single most important female athlete of the 20th century.” That is what PBS, which tonight premieres an American Masters documentary about King, calls the woman who broke extraordinary barriers in sports, business and equal rights for women.