It’s almost too good to be true. Could cinema be witnessing the birth of a stunning new mixed doubles partnership? Last year, Korean-Canadian film-maker Celine Song gave us her wonderful, Oscar-nominated debut film Past Lives, a personal love-triangle movie about a South Korean woman in the US, married to a white American writer, poignantly reconnecting with her Korean childhood sweetheart; the fictional writer, incidentally, has a novel out called Boner. Now Song’s actual white American husband Justin Kuritzkes has written this love-triangle movie, an uproarious screwball dramedy of straight sex and queer tennis: one player, incidentally, is renowned for his large penis.

Some day, film school courses will be devoted to parallel-textual analyses of these two films, and maybe the legendary third wheel will come forward with a screenplay satirising sexual stereotypes, about a woman and a man who create a sensitive drama and a macho comedy from the same situation. Challengers is terrifically absorbing and funny, with zinging extended dialogue rallies – though its cop-out ending fudges what we all know about tennis. Like life, it’s a brutal zero-sum game of winners and losers.

Luca Guadagnino directs with style and Zendaya is devastatingly cool as Tashi, a former superstar tennis player turned coach, now married to her single client: Art, played by Mike Faist, whose sensitive, open, boyish face registers the unfamiliar and disagreeable sensation of losing. He is way off his game these days, going out to patently inferior players, and Faist shows how he is perhaps getting tired of the tennis circuit, while glumly sensing that his wife finds this losing streak a serious turnoff. But fiercely focused Tashi comes up with a plan which Art timidly accepts: he will slum it on the inferior ATP Challenger Tour to match with some no-hoper whom he can crush. The taste of winning will get his groove back.

But to his horror – and a more ambiguous emotion from Tashi – Art is matched with his former best friend and Tashi’s ex-boyfriend Patrick, a louchely handsome performance from Josh O’Connor. Patrick has fallen on hard times, sleeping in his car and touring the cheaper circuits, but he has still got the talent. Maybe trouncing Art will impress Tashi, with whom he is, of course, still deeply in love.

Or maybe it’s Art with whom he is still deeply in love. The course of their triangular romance and all its painful, fateful rows and infidelities are cleverly laid out in an exhilarating series of flashbacks and flashforwards, their past lives revealed in sudden hairstyle changes and clothing shifts, with Art and Patrick starting out as gormless teen chumps dazzled by Tashi, and growing near middle age … still dazzled by Tashi, who is charismatic at any age. The tennis itself is very convincingly dramatised and our three heroes really do look as if they are hitting the ball for real.

This is not the rather diffident stroke-play of Kirsten Dunst and Paul Bettany in the quaint, but in some ways comparable, tennis movie Wimbledon from 2004, though the gamesmanship and toxic masculinity reminded me pleasantly of Ian Carmichael and Terry-Thomas trying to impress Janette Scott during the famous tennis scene in the 1960 British classic School for Scoundrels. (Although Scott never encouraged Carmichael and Thomas to snog, while in their hotel room for a three-way.)

Moment by moment, line by line and scene by scene, Challengers delivers sexiness and laughs, intrigue and resentment, and Guadagnino’s signature is there in the intensity, the closeups and the music stabs.

• Challengers is in Australian cinemas on 18 April and UK and US cinemas on 26 April.