If another Gulf war, classic price-gouging tactics and long-distance stadium treks have you down about this year’s World Cup, consider the alternative from the director who gave us Dumb and Dumber and There’s Something About Mary. Balls Up is the fourth major feature that Peter Farrelly has helmed solo since he and his brother, Bobby, drifted into separate pursuits. And even though this comedy flies well over the crossbar set by those instant classics, Prime Video at the very least should have given it the chance to stand on its own merits in a theatrical release – where, one suspects, this ribald delight would have had little trouble finding an audience, especially among football fans looking for an escape from the doom and gloom the host nation has brought to this year’s tournament.

A note of caution to viewers who think they may have time to build up to show-stopping hair gel-style gags: this buddy comedy is filthy right out of the gate. (Welcome to the streaming era!) Paul Walter Hauser is Elijah, the sheepish product designer exec behind a revolutionary, testicle-shrouding male prophylactic that his teetering company is trying to position as the World Cup’s official condom. Mark Wahlberg is Brad, the hotshot salesman who closes the deal with the Brazilian travel ministry, then promptly blows it by seducing the cabinet minister, Santos (Benjamin Bratt), into an innocent toast that triggers a relapse from nine years of sobriety, culminating in an 8-ball rager that goes viral.

Santos is fired by Lula, the 80-year-old Brazilian president who livestreams his workouts (true story). The condom company is ruined, and the boss (Molly Shannon) lays everyone off. But Elijah and Brad receive something of a golden parachute in the form of VIP tickets to the World Cup final that Santos set up for them before falling off the wagon. But before long, the ad men foul that sweetheart deal up by drunkenly scrambling on to the pitch in extra time and thwarting a goal that would have leveled the match for the host country – making them official enemies of the state. From there, the race is on to get out of the country in one piece – or at least before the Americans tear each other apart first.

In general, there’s much to detract from Wahlberg’s overall star quality: the Boston smugness, the creatine personality, the culture-vulture origin story. But damn if he isn’t one of the finest straight men of his generation – and first among hunks when it comes to playing against type. (Action stars aren’t supposed to whine, and yet Wahlberg is somehow so winsome when he isn’t getting his way.) His chemistry with Hauser, a mainstay in the Jesse Plemons league of shapeshifters, recalls his best work alongside Will Ferrell in The Other Guys.

And it’s hardly overshadowed by the other scene chewers in this R-rated free-for-all. Shannon’s knack for playing women of meager self-awareness remains as strong as it was in her SNL prime. Bratt is a total surprise, and a hoot, playing a native Brazilian. And Sacha Baron Cohen, who plays a roguish cartel boss named Pavio Curto Bündchen (and the family resemblance is unmistakable once you spot it), makes a meal out of the languid, trombone-like vowels of Portuguese-language speech. It puts extra pressure on our bumbling heroes to listen closely and follow instructions – or wind up in the “mass gravy” by the backyard pool.

Balls Up is juvenile entertainment, handled by professionals. No, Paul Wernick and Rhett Reese, the scriptwriters, can’t resist the low-hanging fruit, down to the literal bananas. But as with their Deadpool work, they layer it with compounding stakes, spicy dialogue and characters with no sense of their own humor. For my money, though, the real hero is Dave Palmer, the composer, who classes up the whole raunch-fest with vintage samba and bossa nova sounds.

Comedy films will only get harder to dial in as tastes diverge and the mass media experience grows ever more siloed and bespoke. But this addition to the Farrelly brothers’ canon feels like the kind of comedy auteurs and fans are always saying “you can’t make any more”, even with a star and a director who could draw a crowd by themselves. In an alternate universe, this would kick off the summer blockbuster season. But on this timeline, the suits at Amazon have shown, yet again, they clearly don’t have the … well, you know.

• Balls Up is available now on Prime Video