A couple of weeks ago, Steven Spielberg praised the new movie “One Battle After Another” after an advance screening, using the words “incredible” and “insane” to describe its tale of modern-day American revolutionaries. Let me add the following to those apt descriptors of the picture: shambolic, perverse, provocative, and exhilarating. 

Directed by Paul Thomas Anderson, the big-budget movie’s sprawling story and ensemble cast hark back to his early successes like “Boogie Nights.” On the other hand, it resumes the auteur’s contained examinations of power and opposition, as reflected in works such as “There Will Be Blood” and “The Master.” That its depiction of a band of rebels co-exists with an exploration of two characters who are ideologically at odds makes for an experience that can feel unfocused and disjointed, to say nothing of its tonal swings. 

Yet given that the two roles are played by Leonardo DiCaprio and Sean Penn, one isn’t too bothered by the film’s chaos, just happy to go along for the ride. 

And what a ride it is. Beginning with a tense raid on an immigration detention center near the U.S.-Mexico border and climaxing with a thrilling car chase on a southwestern highway of rolling hills, the picture’s narrative is nearly relentless. Its first half, in particular, hardly ever stops to take a breath, as we’re immersed in the activities of an insurgent group called the French 75. Chief among them is troublemaker Perfidia (Teyana Taylor), who’s in a relationship with explosives expert Bob (DiCaprio). The collective advocates for open borders and rails against a “fascist,” “imperialist” government. In addition to freeing detained immigrants, its members bomb buildings, forewarning authorities to avoid killing or injuring bystanders. 

Sex and violence are bluntly but amusingly aligned in short moments showing Perfidia and Bob fooling around before, after, and sometimes during their criminal activities. This kinkiness extends to scenes with Mr. Penn’s Lockjaw character, a colonel who is initially toyed with by the revolutionary vixen and subsequently falls for her when they meet regularly and clandestinely. Later, after she gives birth to a daughter, shoots a security guard, and is captured by the police, Lockjaw offers her the chance to work with the federal government by ratting out some of her comrades. Perfidia soon exits the story, though the character’s sense of freedom and Ms. Taylor’s dynamic aura are not easily forgotten. 

Once the movie shifts to 16 years later, the frantic editing and storytelling — which feel like a preamble to the real narrative — slows down a bit, with Messrs. DiCaprio and Penn given more sustained attention. Living in hiding with Willa, Perfidia’s daughter, Bob is now a middle-aged slacker who has no reason to wonder whether she is his daughter, as he knows nothing of his former partner’s affair. Lockjaw, meanwhile, seeks a higher social status by becoming a member of a secret society of elite white men who believe in racial superiority.

With Willa’s paternity unclear, and with Lockjaw determined to erase any potential trace of his dalliance with her mother, the military official engineers a way to catch the teenager and Bob through his official duties. Thus begins the third act, yet it often feels like the two-and-a-half-hour film has no structure. This bagginess may reflect the novel on which it’s loosely based: Thomas Pynchon’s “Vineland.” It also shows how Mr. Anderson was unable to meld the material, his sensibilities, and the demands of an action movie featuring major stars into a carefully crafted whole. 

Mr. DiCaprio draws on his real-life persona as a good-time guy for the part of Bob, and the director seems to indulge the actor, particularly in an extended sequence in which the character has to recall codewords. Welcomely, the famous bachelor also brings his emotional immediacy to the fatherly moments, with newcomer Chase Infiniti playing a clear-eyed Willa.

It’s Mr. Penn’s performance, though, that will be the most talked about. With a smallish head on a built-up body, the actor isn’t afraid to come off as ridiculous, though his send-up of military and macho stereotypes nearly ends up as caricature. What a pity that he never shares any screentime with Mr. DiCaprio, as their characters represent the film’s central tension — who is Willa’s father — and epitomize two contemporary modes of masculinity. 

Although mostly compelling, the film never establishes a consistent “dark comedy” tone, with composer Jonny Greenwood’s frequently atonal and overused score not helping matters. Nutty moments, popular songs, Benicio del Toro’s wry detachment, and semi-clever dialogue indicate satire; while sober scenes, jarring violence, Regina Hall’s gravitas, and topical relevance suggest serious drama. Countless cultural references and the use of stoner humor point to how the movie is a college boy’s idea of entertainment.

The film’s most trenchant observation connects the “Great Replacement” theory with America’s history of racial violence and fear of miscegenation. And there’s no denying that its look at a present-day police state palpitates with fury and subversive energy, though Mr. Anderson also includes instances in which the preciousness of the left is mocked. Still, in the end, the director could be said to fight off an allegorical interpretation of his film through its various shenanigans and action setpieces, retreating to a more mythic, interdependent battlefield of cat and mouse, rebel and traditionalist, chaos and order.