We should all be happy that Bryan Cranston has become a highly sought-after movie actor. Yet the very thing that brought him to that position — the pop-culture quake that was “Breaking Bad” — has now given him the ultimate tough act to follow. How do you top, or even rival, what he accomplished playing a gentle-souled family-man chemistry teacher who turns himself into a violent drug badass? “The Infiltrator,” a sensationally intelligent and exciting true-life thriller directed by Brad Furman (“The Lincoln Lawyer”), offers the answer: Have him play a gentle-souled family-man law enforcer who goes undercover as a money launderer to Pablo Escobar.

Robert Mazur, the man Cranston plays in “The Infiltrator,” actually did that. In 1986, he realized that the war on drugs was going after the wrong target — the drugs themselves, massive shipments of cocaine that even if seized could be replaced within days. Mazur figured out that the infinitely smarter thing to do would be to follow the money, which could lead directly to the kingpins who controlled everything. And so he came up with a sting operation that was built around creating a flamboyant alter ego for himself: Bob Musella, a jaunty, high-rolling businessman who launders mountains of drug-cartel cash — tens upon hundreds of millions — by promising to hide them in a network of legitimate investments. He doesn’t just work with thugs and drug lords; he deals with respectable international bankers, setting up a vast network of corruption that is winked at by governments. It’s like an underworld rehearsal for the new global money culture.

To do all this, Bob Mazur had to be a master deceiver. That’s the shivery fascination of the whole undercover-cop genre — that it’s about law enforcers who, in essence, turn themselves into actors, and the stakes are such that they need to be giving an Academy Award performance at every moment, or they’re going to blow their cover and die. It’s a savory thing to watch an actor play a cop who really has to be an actor, improvising his way through one scary existential situation after another. Don Johnson had a lot of great moments doing it on “Miami Vice,” and when you think back to the Johnny Depp performances that were still rooted in the real world, certainly one of the highlights was his intricate and mournful work as the undercover cop in “Donnie Brasco.” But in “The Infiltrator,” which is based on Mazur’s memoir (adapted into an ingeniously layered script by Ellen Brown Furman), Bryan Cranston gives the most authentic and lived-in performance as an agent pretending to be a criminal that I have ever seen.

Part of Cranston’s magic as an actor is that he’s drawn to playing men of extreme volatility, but he exudes a deep core of decency; it’s as if the De Niro of the ’70s had been infused with the soul of Henry Fonda. In “The Infiltrator,” the grand irony is that it’s Cranston’s homespun, folksy-guy quality that makes Bob into such a brilliant undercover agent. He establishes his fake identity by literally setting up the shell of an investment company, and he turns the character of Bob Musella into a glad-handing financial player in silk pin-stripe suits, all bluster and sharky grins, but what makes the impersonation convincing is the way that he gets right onto the wavelength of the people whose trust he has to win. He connects with two scuzzy veteran drug peddlers who are on the lower middle rungs of Escobar’s organization, and he draws on his essential inner nice-guy-ness to flatter and cajole them. He knows how to make people feel good, and that, as the movie demonstrates, will take you far.

Bob’s decency can also be a trap. Partying at a strip club with his new associates, he has to go along with them and get a lap dance, but he draws the line at sleeping with a stripper (because he doesn’t want to betray his wife). He makes the excuse that he has a fiancé, but this looks, at first, like a bad mistake, which raises the haunting issue: How far into his role does an undercover agent really have to go? There’s a great scene in which Bob’s cover is nearly blown, and without taking even a moment to think about it, he pushes himself to extremes to save himself. He is out at a restaurant with his wife — his real wife — to celebrate their anniversary. Suddenly, he spots one of his new drug associates, and his two worlds come crashing together. What can he do? Instantly, he slips into character by summoning the waiter and hurling obscenities at him for bringing the wrong cake, but he knows even that isn’t going to be enough to fool anyone, so to kick up the tantrum another notch, he smashes the waiter’s face down into the cake. Bob’s wife has never experienced this side of him (she knows what his job is, she just hasn’t seen it), and it’s as if she’d suddenly witnessed her husband turning into De Niro’s Al Capone in “The Untouchables.”

“The Infiltrator” glides from New York to Miami to Panama to Paris, and it often takes a moment to figure out where, exactly, you are, but that’s by design. The idea is that it’s really all one place, a stratosphere of luxe rotting corruption connected by private plane. Bob acts his way through one devious encounter after the next, working his way up the chain of Escobar’s organization. The men he meets are seasoned killers who gleam with animal awareness, and that’s part of what lends the scenes their danger; the men all look at Bob as if they could see right through him. There’s the supremely creepy Escobar money manager, Javier Ospina (Yul Vazquez), who’s like a crazy Dean Stockwell character; he comes on to Bob — he comes on to just about everyone — and then sketches his ominous, lingering skepticism about the organization’s new financial planner into little drawings on cocktail napkins. There’s the henchman who Bob wins access to only by sitting through a bizarre voodoo ritual that results in the stranger alongside him being shot in the head. Bob, with good reason, thinks he’s going to be next.

When enough time has passed, Bob wins a hallowed meeting with Escobar’s suave lieutenant, Roberto Alcaino (Benjamin Bratt), and before he knows it they’ve become back-slapping friends. Bob now has a “fiancé,” played by a fellow undercover agent, Kathy Ertz (Diane Kruger), who has never been on a mission before. The two have to pretend to be a sexy globe-trotting couple, and the fascination of their scenes is watching the mixture of caution and daring — sticking to their script, but also taking off from it — that fuels the intensity of their impersonation. Kruger, who has always been a dynamic actress, here performs with a luminous sensuality that she turns on and off like a light switch. As a cop, she’s all no-nonsense professionalism, but the nature of the “bond” that she and Bob forge with Roberto and his wife, sitting in their dazzling Miami penthouse, is that it demands a layer of intimacy. The scenes between the four of them play like a tango of fear and emotion. The two agents begin to drift, ever so slightly, into living out their roles — not in a way that’s corny or unbelievable, but in a way that allows the audience to register their attraction as something that’s never stated. It emerges from the charged anxiety of the situation.

“The Infiltrator” creates enthralling suspense out of the drama of what undercover agents do, and there isn’t a moment in it that makes the danger looks falsely seductive. The power of Cranston’s performance is that he captures the deep anguish that deep cover can bring. Kruger matches him, beat for psychological beat, and John Leguizamo gives a pinpoint performance as Bob’s low-life informer colleague, whose slovenly flakiness turns out to be, itself, a kind of cover. As Roberto, the courtly Colombian domestic sociopath, Benjamin Bratt acts with a new command, truly convincing you that he’s a heartbeat away from Escobar, the most ruthless man on the planet. A quibble one might have with “The Infiltrator” is that Furman’s visual style as a director, while crisp and eloquent, never transcends a kind of medium-shot conventionality; the scenes are gripping, but they don’t soar. (The closest the film comes to that is the heart-in-the-throat moment when Bob’s briefcase with the hidden tape recorder pops open.) Then again, that’s all intrinsic to the movie’s taut power. You could almost say that the style of “The Infiltrator” is a perfect mirror of the undercover agents it’s about, who have to do all sorts of amazing and terrifying things while keeping their souls meticulously under wraps.