“You’ve come a long way baby, to get where you got to today,
you’ve got Virginia Slims now baby, you’ve come a long, long way.”
– Ubiquitous commercial jingle for Virginia Slims cigarettes, targeted to the female smoker

Bobby Riggs vs. Billie Jean King.

A self-promoting, long-retired male pro given to statements such as, “I like women in the kitchen AND the bedroom,” taking the court against a charismatic, fiercely competitive female star at the top of her game.

What, you thought Mayweather/McGregor was the first manufactured sporting spectacle in American history?

“Battle of the Sexes” stars Emma Stone as Billie Jean King and Steve Carell as Bobby Riggs. Neither star bears much of a natural physical resemblance to the characters they’re playing — but thanks to the award-level makeup and wardrobe, and even more thanks to the remarkable performances, the transformation of these two is astonishing.

These actors aren’t doing impersonations. They’re creating full-fledged, complex characters — each flawed, each making missteps that hurt others, but both quite sympathetic and endlessly fascinating.

Whether you know every detail of the Riggs/King matchup and you remember watching it in the Astrodome or on TV (more than 90 million viewers tuned in for the live broadcast) or you’ve never even heard of this crazy but in its own way important chapter in sports history, “Battle of the Sexes” stands on its own as a finely tuned period piece, a vibrant comedy, an effective character study and, yep, an inspirational sports movie.

The year was 1973. “The Women’s Liberation Movement” had made strides on numerous fronts in the 1960s and early 1970s — but the aging-lion “Mad Men” males from the previous generation were still in firm control of everything from politics to business to the media to sports.

Including women’s tennis.

The prize money for the major events on the men’s tour was eight or 10 times as much as the pool for the women. When the leading players on the women’s tour rebelled against the establishment and established their own tour, the sponsor was a cigarette: Virginia Slims.

Sometimes progress comes with a raised eyebrow.

Directors Jonathan Dayton and Valerie Faris (“Little Miss Sunshine”) and screenwriter Simon Beaufoy expertly alternate between the stories of Billie Jean King and Bobby Riggs, which take place on parallel tracks for the first half of the film.

As Billie Jean and World Tennis Magazine founder Gladys Heldman (Sarah Silverman, displaying her usual exquisite and acid-tongued timing) lead the charge for the female players to break away from the Association of Tennis Professionals and its chauvinistic leader Jack Kramer (Bill Pullman), the late-middle-aged Riggs is adrift.
Bobby has an office at the company owned by his wealthy father-in-law, but there’s no real job to accompany the paycheck. He has promised his long-suffering wife Priscilla (Elisabeth Shue) he’s given up gambling — but many a night he finds an excuse to get out of the house and go to the country club, where he hustles rich guys on the tennis court with a variety of outlandish proposition bets.

Before “Battle of the Sexes” gets to, well, the battle of the sexes, it’s a thoughtful and sometimes heart-wrenching study of two marriages in crisis. Priscilla doesn’t want to give up on Bobby, but she’s tired of the gambling and the Peter Pan act.

Meanwhile, Billie Jean for the first time in her life is acknowledging her sexual orientation. To the outside world, Billie Jean is happily married to the loving and loyal and supportive Larry (Austin Stowell), who also manages her career, but she has privately embarked on a passionate love affair with her hairdresser, Marilyn (Andrea Riseborough). To say this was a potentially career-destroying undertaking in the early 1970s is an understatement.

Bobby’s the one who comes up with the idea of a publicity stunt/exhibition match in which he’ll play the part of the sexist pig, grunting and bellowing about women as the inferior sex, taking on a top-ranked female player.
 First he takes on Margaret Court (Jessica McNamee), who was actually the top-ranked women’s tennis player in the world at the time — and he humiliates her, getting in her head from the start of the match and taking her down in straight sets.

Now Billie Jean, who had been adamantly opposed to taking the court against the Court Jester, feels compelled to accept Riggs’ challenge, lest he turn women’s tennis into a joke.

“Battle of the Sexes” is told mostly from the point of view of Billie Jean King. (If Carell gets the awards consideration he deserves, it should be in the supporting category.) Fresh off the Oscar for “La La Land,” Emma Stone does the best work of her career. Her Billie Jean King is a champion on multiple levels. It’s a spectacularly good portrayal of one of the greatest athlete/activists in American sports history, who displayed grace and dignity and a sense of humor and an enormous heart even when she was in the middle of a circus.

★★★1⁄2

Fox Searchlight presents a film directed by Valerie Faris and Jonathan Dayton and written by Simon Beaufoy. Rated PG-13 (for some sexual content and partial nudity). Running time: 121 minutes. Opens Friday at local theaters.