Pictures with “troubled” production histories usually turn out badly, but there are exceptions to the rule, and Marc Forster’s loose adaptation of Max Brooks’ best-seller is one of them. Despite release delays and reports of major rewrites, reshoots and post-production tinkering, “World War Z” turns out to be, despite a huge budget, a lean, mean zombie machine that builds enormous tension by speeding through a succession of nail-biting set pieces and shows signs of misguided tweaking only in a closing montage that ends the picture on a flat note.

A sort of big brother to “28 Days Later,” the film postulates the outbreak of a world-wide epidemic that turns those bitten by the already-infected into ravenous “undead” in a mere ten seconds or so. Forster and his screenwriters waste no time in setting the plot in motion, thrusting Gerry Lane (Brad Pitt), his wife Karen (Mireille Enos) and their two young daughters (Sterling Jerins and Abigail Hargrove) into a traffic jam in downtown Philadelphia that turns into a zombie-driven riot. Lane, who’s given up a job as a United Nations investigator to spend more time with his family, contacts his former boss Thierry (Fana Mokoena), who arranges for their extraction from the roof of a nearby high-rise—which requires their surviving a race up the stairwells with the undead in full pursuit.

Taken to an aircraft carrier that’s serving as the international command center for response to the contagion, Lane is persuaded to head to Korea and seek the origin of the plague. Andrew Fassbach (Elyes Gabel), the scientist he’s accompanying—the great hope of the expedition—proves less efficient than desired (only the first instance in which the film upends expectations), but Lane is given a hint by an imprisoned CIA agent (David Morse) and soon is off to Jerusalem, which is using its security walls to provide a sanctuary for the unaffected and where he confers with the Mossad agent (Ludi Boeken) in charge of the operation. From there he’s off on a harrowing flight to a W.H.O. facility in Wales, accompanied by a wounded Israeli soldier (Daniella Kertesz), where he persuades the staff to attempt a dangerous test that won’t end the epidemic, but could afford mankind a modicum of defense against the zombies. Unfortunately, putting his plan into effect requires a nerve-wracking incursion into a part of the complex filled with undead workers, all poised to attack at the drop of a pin since they’re attracted by sound.

Even if you find the story’s premise pretty preposterous, it’s undeniable that Forster, working closely with cinematographer Ben Seresin and editors Roger Barton and Matt Chesse, has fashioned a chain of action sequences remarkable for the suspense and sudden shocks they generate. Some are very large-scaled—the initial Philadelphia melee, the Jerusalem rampage. Others are more confined—the escape at a Korean airport, that frightening flight to Wales. And others are practically claustrophobic, like the last-act intrusion of the undead hive at the W.H.O. facility. Forster stages all of them with remarkable skill, drawing incredible payoff from the sudden ringing of a phone, the sound of glass crunching underfoot or the clatter of a soft drink can kicked across a floor. And when special effects are called for, the behind-the-scenes crew delivers convincingly, with zombies that are individually pretty gruesome and collectively swarm like insects in search of prey in sequences that are positively epic in scope.

Pitt anchors the film with a performance that cannily conjoins his matinee idol persona with a scraggy everyman look. No one else gets a great deal of screen time—Matthew Fox, for instance, is virtually unrecognizable—but each supporting player maintains the straightfaced, almost documentary tone that keeps things from descending into unintentional comedy. (In fact, the jokes are few and far between here, with those that are present having a distinctly grim underpinning, like a throwaway explanation for how North Korea suppressed the infection within its borders, even though the rationale doesn’t make much sense.)

The secret to the success of “World War Z” is twofold. On the one hand, it plays the story straight, eschewing the tongue-in-cheek approach that must have been a strong temptation in today’s movie marketplace. And on the other, it hurtles along at a headlong pace, keeping quiet interludes—even those involving the Lane family—to a minimum and getting them over with quickly. The breathlessness of the approach is key to the movie working—and in retrospect, no one should care that it took some delay, rethinking and even reshooting to achieve it. The end result might be too grim and downbeat to match the popularity of more gung-ho, triumphant apocalyptic thrillers, but in quality terms it puts most of them to shame.