“Battle of the Sexes” a relevant retelling

★★★5 Rated PG-13. 121 minutes.

At a time when Venus and Serena Williams reign supreme — and seem to have done so forever — it’s difficult to visualize a time when the fight for gender equity in tennis was frontpage news.

But Jonathan Dayton and Valerie Faris bring that era to life with verve and humor in “Battle of the Sexes,” a warm, earnestly entertaining film that revisits a pivotal 1973 match between a 55-year-old former Wimbledon champion named Bobby Riggs and 29-year-old tennis star Billie Jean King.

The showdown — hyped to hell and back before being staged at the Houston Astrodome — was comeuppance in the form of performative kitsch, with the competitors arriving in the midst of Vegaslike fanfare and gaudy retinues (leggy ladies for Riggs, bare-chested men for King). For weeks, Riggs, a notorious hustler, had been partying, pulling off stunts and playing the media instead of practicing.

King, the bespectacled, intensely focused workhorse, had been busy working out, honing the precision shots that would prove lethal to her opponent’s shockingly lethargic game. She beat him in straight sets, winning the $100,000 prize money and striking an epochal blow for women’s rights that made her an instant feminist icon.

“Battle of the Sexes” looks beneath the ballyhoo and horsing around to provide context on the heightened stakes that informed Riggs and King’s confrontation. Portrayed in an uncannily spot-on impression by Steve Carell, Riggs comes across as a compulsive gambler eager to reclaim the spotlight and save his marriage. (Elisabeth Shue delivers a dignified, quietly bemused performance as his wife Priscilla). Carell and the filmmakers are clearly having a ball as they recreate Riggs’ famous exhibition games, in which he handicapped himself by dressing as Bo-Peep (complete with live sheep) and playing with skillets instead of rackets.

For her part, King — played in a less physically convincing but quietly sympathetic turn by Emma Stone — wasn’t explicitly political at all. She was simply interested in getting equal pay on the tennis circuit. But when she establishes an instant erotic connection with a hairdresser named Marilyn (Andrea Riseborough), she realizes that her sexual orientation may jeopardize the progress she’s been working for.

Best known for their dysfunctional-family comedy “Little Miss Sunshine,” Dayton and Faris skillfully delineate the personal issues that were riding on the match between “the lobber and the libber,” as Riggs and King were dubbed, introducing a possibly malign presence in the form of a judgmental Margaret Court (Jessica McNamee) and an outright villain in the form of protour chief Jack Kramer (Bill Pullman).

And they brilliantly lean in to the titular battle as a camp event, casting an ensemble of gifted comic actors in supporting turns that crackle with winking good fun: Alan Cumming, Chris Parnell and Fred Armisen are all on hand in small but crucial roles, but Sarah Silverman is particularly delicious as Gladys Heldman, the spiky, chainsmoking publicist for King’s newly established Women’s Tennis Association.

Tricked out with sprightly period detail — down to the Robert Redford sideburns of King’s handsome husband (Austin Stowell) and the terrific 1970s soundtrack — “Battle of the Sexes” is a pleasure to watch, both as a nostalgia trip and collection of pop artifacts.

When the big night finally arrives, the actual tennis is a relative letdown. The filmmakers don’t address long-held rumors that Riggs threw the game to pay off gambling debts. But what’s most astonishing and memorable about the climactic sequence is the filmmakers’ use of actual footage of ABC’s Howard Cosell delivering a steady stream of patronizing remarks about King’s abilities and attractiveness.

Riggs, however, is depicted less as a genuine sexist than as a bumbling ally, his outrageousness a matter of showmanship rather than animus.

Therein lies the touching subtext of “Battle of the Sexes,” which is almost remedial in its timeliness, given last year’s political grudge match.

It gives audiences a glimpse of where we’ve been, how far we’ve come and, soberingly, how far we’ve yet to go — especially when we’re with her.