The women’s rights event of the early 1970s that captured the most attention worldwide wasn’t in 1971 when Helen Reddy sang “I Am Woman.” Or 1972 when Gloria Steinem founded Ms. Magazine. Or even the day in 1973 when Congress passed the Equal Rights Amendment.

The big event was a publicity stunt broadcast worldwide that fall.

A record 50 million Americans tuned in to see the much ballyhooed tennis match between 55-year-old Bobby Riggs, a former champ turned self-proclaimed “male chauvinist pig,” and Billie Jean King, 29, the No. 1 ranked women’s player, who insisted that men and women should compete on a level playing field. Watching inside the Houston Astrodome were 30,000 spectators. To the victor would go the winner’s trophy, a $100,000 prize and lifelong acclaim.

Rather than try to wring artificial suspense out of the competition’s well known outcome — spoiler alert: King won — “Battle of the Sexes” looks at the issues of feminism and chauvinism with almost equal sympathy for King (Emma Stone), Riggs (Steve Carell) and most of the supporting characters.

The directing team of Jonathan Dayton and Valerie Faris (“Little Miss Sunshine”) know how to charm viewers, render offbeat personalities relatable, make ’70s wardrobe look appropriately laughable and send audiences home happy.

The script by Oscar winner Simon Beaufoy (“The Full Monty,” “Slumdog Millionaire”) holds social statements largely in check. For a sports biographical story like this, that’s enough.

The film opens with King at a milestone in her career, winning the U.S. Open women’s singles championship and becoming the world’s top-ranked female player.

Her triumph doesn’t carry much weight off the court, however. The tennis establishment, headed by retired pro Jack Kramer (Bill Pullman), paid male winners eight times as much as their female counterparts. “Men are more of a draw; the men are simply more exciting to watch,” says Kramer, the kind of man who calls a waitress “hon.” Frustrated by his hardheaded refusal to address the disparity, King creates her own women’s circuit with eight other players.

Winning sponsorship from Virginia Slims cigarettes is an awkward step forward; despite raised eyebrows among health advocates, King’s manager (Sarah Silverman) encourages the sisterhood to puff it up for the cameras in public. The tobacco company covers the women’s expenses as they travel between tournaments.

It’s on one of those cross-country trips that King, who is tightly wound and shy off the court, meets Marilyn Barnett (Andrea Riseborough), a hairstylist with a flirtatious vibe. Barnett’s stroking of King’s hair triggers unexpected sensations and leaves her wanting much more.

Soon they’re lovers traveling together and sharing hotel rooms while King keeps their relationship hidden from her mild-mannered, stay-at-home husband, Larry (Austin Stowell, giving three-dimensional humanity to a challenging role).

The film’s title refers to the personal battles the characters face, portrayed dramatically where King is concerned. Her former rival, Australian star Margaret Court (Jessica McNamee), joins the women’s circuit as the only mother and the only player traveling with her spouse.

When she condemns the “licentiousness, immorality and sin” that all-female sports teams build up, it’s clear whom and what she’s talking about. Then the sponsors’ reactions if King were to be outed enter the mix.

Thankfully, the film makes the ever hustling Riggs, gifted at winning bets and clumsy at retaining relationships, into a cartoon of broad comedy. It’s ideal casting for Carell, who perfectly captures the irregular, energetic body language and looks like Riggs’ clone.

His struggle concerns his heiress wife (Elisabeth Shue), who adores his freewheeling humor but is appalled by his chronic gambling. He goes through the motions of attending Gamblers Anonymous meetings but turns them into a hullabaloo, and he has a remarkably crafty grip on his psychologist. His closest friend is a freelance pharmacist (Fred Armisen), who gives Riggs piles of mysterious get-up-and-go pills as the big match nears.

Riggs proposes the televised tennis showdown for loads of money from sponsors; King accepts his mock-misogynist challenge for the principle of the thing. Their climactic faceoff is well enough staged by stunt doubles shot from afar, with occasional glances at the stars.

The real excitement comes from watching the athletes’ families in the stands pulling for them to win. And anonymous characters like the woman who holds aloft a sign that reads “Billie Jean for President.” It’s 44 years later, but much of it is as relevant as ever.