Like Billie Jean King’s tennis game, the joyous movie “Battle of the Sexes” covers every inch of the court — as an inspirational sports drama, as a riotous comedy, as a tender romance and as an insightful biography of King and her pivotal role in the fight for women’s equality.

Part of that role was a symbolic one, culminating in the event of the movie’s title, the 1973 exhibition match between King, then the best women’s player in the world, and Bobby Riggs, a former Wimbledon and U.S. Open champ who at 55 remade himself as a hustler determined “to put the ‘show’ back in ‘chauvinism.’”

King is beautifully played by Emma Stone, who nimbly captures the tennis star’s lithe athleticism and her no-nonsense determination to prove herself equal on the court and off. Riggs is played hilariously by Steve Carell, who revels in the blowhard Riggs’ clownish persona and constant need to make a buck. Carell and Stone — who played father and daughter in 2011’s “Crazy, Stupid, Love.” — here have a prickly chemistry that plays up the gender and generational differences between the two.

As the limber script by Simon Beaufoy (“Slumdog Millionaire,” “The Full Monty”) progresses, King is in the middle of two other battles. One is her demand to Jack Kramer (Bill Pullman), the tennis legend and now head of the sport’s U.S. governing body, that women players get paid what the men do. When Kramer rebuffs King, she responds by launching a rival body, Women’s Tennis Association.

The other battle is an internal one, as King — married to her college sweetheart, Larry (Austin Stowell) — begins to realize she’s attracted to women. When she meets a hairdresser, Marilyn Barnett (Andrea Riseborough), the romantic sparks become overwhelming. They also become a distraction when King is playing on the just-formed Virginia Slims circuit, where her main competition is the Australian star Margaret Court (Jessica McNamee), a devout Christian who takes a dim view of homosexuality.

Married directors Jonathan Dayton and Valerie Faris (“Little Miss Sunshine,” “Ruby Sparks”) shift between the story’s many moods so gracefully it feels effortless. One minute Riggs is mugging for the cameras, the next King and Marilyn are sharing a passionate bedroom scene, and soon the action is back on the court. Dayton and Faris weave all the plot threads — as well as the ’70s period details, from disco balls and bellbottoms to the wooden-racket tennis moves — into an exuberant whole.

The movie fields a solid supporting cast, led by Sarah Silverman as King’s hard-charging business manager Gladys Heldman. Also notable are Natalie Morales as tennis cohort Rosie Casals, Elisabeth Shue as Riggs’ wealthy and indulgent wife, Priscilla, and Alan Cumming as a fashion designer who becomes King’s confidant.

“Battle of the Sexes” ultimately succeeds for the way the filmmakers and Stone winningly convey how King, in the middle of a media circus and with her professional and personal life in turmoil, came through it all with the Astrodome-sized heart of a champion.

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’Battle of the Sexes’

The famed tennis duel between Billie Jean King and Bobby Riggs becomes a springboard for a rich story of equality, professional struggle and personal heartache.

Where • Theaters everywhere.

When • Opens Friday, Sept. 29.

Rating • PG-13 for some sexual content and partial nudity.

Running time • 121 minutes.