PARIS — Lucie Safarova triumphed over her nerves Thursday, Serena Williams over her health.

Now, they will meet in the French Open women’s final.

It is an unexpected matchup for Williams, the undisputed No. 1 player in women’s tennis, as she takes aim at her 20th Grand Slam singles title.

But Safarova, a Czech veteran who will be playing in her first major final at the advanced tennis age of 28, has certainly earned her spot.

Seeded No. 13, Safarova has made her own luck at Roland Garros, sweeping through a brutal draw without the loss of a set. On Thursday, she defeated seventh-seeded Ana Ivanovic, 7-5, 7-5, keeping her cool and securing the victory after double-faulting on her first match point and failing to hold her serve.

“I was really like overthinking and couldn’t really concentrate to be there in the moment,” Safarova said of that lost service game.

It is one of the great challenges of tennis, a sport in which there is so much time to think: on the changeovers, between points, between serves.

It has been a shaky French Open for Williams, and she wobbled plenty more against the clever, determined Timea Bacsinszky. Apparently ill, Williams looked on the verge of toppling over on the clay on several occasions, but she generally looked much more stable when the ball was in play.

She had lost the first set in three consecutive matches before defeating Sara Errani in straight sets in the quarterfinals. But Bacsinszky, the No. 23 seed playing in her first major semifinal, put Williams in a hole again, winning the first set, 6-4, and going up a break of serve at 3-2 in the second.

Despite reaching for her ice towel like a lifeline on changeovers and occasionally dribbling balls off her feet as she prepared to serve, Williams swept through the next 10 games to win, 4-6, 6-3, 6-0.

When Bacsinszky’s last shot sailed long, Williams turned slowly and looked at her coach, Patrick Mouratoglou; her mother, Oracene Price; and others in her box, appearing more relieved than delighted.

She then cut short her postmatch interview on court because of a coughing fit, gathered her equipment and walked slowly toward the exit.

Williams, 33, will now have a chance to win her third French Open championship after her titles in 2002 and 2013. If healthy (and maybe even if not) she will be the heavy favorite against Safarova, whom she has beaten in all eight of their previous matches.

“That’s true,” acknowledged Rob Steckley, Safarova’s coach. “But we’re getting closer every time.”