(USA) Sci-fi/Comedy/Action. Directed by Barry Sonnenfeld. Starring Will Smith, Josh Brolin, Tommy Lee Jones, Jemaine Clement, Michael Stuhlbarg, Emma Thompson. Category IIA. 103 minutes. Opened May 24.

The series’ painfully uninspired last outing and the following 10-year hiatus foredoomed “Men in Black III” to total irrelevance and sparked little anticipation, but all it takes is a time-traveling twist and a scene-stealing Josh Brolin to turn a curse into a blessing. Helmed again by MIB resident director Barry Sonnenfeld, the franchise’s latest installment, despite its many (visible but not distracting) flaws, is an all-around entertaining romp. With a spirited production, an on-the-money cast and some effective cornball humor, the film serves as a neuralyzer that can erase your vague yet clearly unpleasant memories of “MIB 2.”

Will Smith and Tommy Lee Jones reunite to play the titular shade-wearing, alien-tracking secret agents: the chipper Agent J and his laconic, enigmatic veteran partner Agent K. When the movie’s arch-villain Boris the Animal (Jemaine Clement from “Flight of the Conchords”)—a nefarious extraterrestrial serial killer with one missing arm—escapes from a lunar prison in the prologue, the mismatched duo is on a routine raid in a downtown Manhattan Chinese restaurant that’s… well, let’s just say not as Chinese as we expected. The bad news comes that Boris has found a way to time-travel back to 1969—the year when he lost an arm and his freedom to K—to kill his nemesis before it all happened and to launch a massive invasion of Earth. For some weird reason that doesn’t hold up even within the film’s own absurdist logic, K vanishes from the present day, and J is the only one among all of K’s colleagues to have survived the temporal displacement and to acknowledge K’s existence over the last 40 years. Now he too has to take a trip—Marty McFly-style—back to 1969 in order to save the life of the young K and take down Boris, once and for all.

After an eye-popping leap off the Chrysler Building, we enter the colorful 60s, where J finds a 29-year-old and less-stony-faced version of his partner, ironically played by 44-year-old Josh Brolin. Bearing an uncanny resemblance to Jones, Brolin does his own special effects in this CGI-fueled movie by flawlessly channeling the former’s mannerisms and Texan drawl (his roles in “No Country for Old Men” and “W.” have probably prepared him for this) that go way beyond simple mimicry. His deadpan charisma delivers understated hilarity, while his clash with the animated Smith is the source of many laugh-out-loud jokes.

Screenwriter Etan Cohen (“Tropic Thunder”) also goofs on the hippie era, poking fun at the fashion industry, pop art and even rock n’ roll. We learn that all supermodels are non-Earthlings (I knew it!), that Andy Warhol (Bill Hader doing a hilarious caricature portrait) is actually Agent W using his world-class artist persona as a cover and that there’s a reason to Mick Jagger’s infamous early promiscuity. At Warhol’s Factory, the pair meets Griffin (Michael Stuhlbarg of “A Serious Man” fame), a sweet and quick-spoken alien who can see the future and holds the key to defeating Boris, which involves an epic trespass into the Kennedy Space Center during the Apollo 11 launch. Compared to the others in the dazzling line-up of supporting actors, Emma Thompson and Alice Eve—two fine actresses playing the young and old Agent O, whose romantic history with K is hardly explored—are criminally underused.

Fantastical technologies and a parade of grotesque outer-space creatures are seamlessly brought out by a top-notch CGI job; and the 3D effects are, if not necessary, rather pleasant. The cinematography by Bill Pope (“The Matrix” films) is neat, and the score by Danny Elfman is playfully energized. The script contains a great deal of plot holes, but the perfectly paced film moves swiftly enough that most of them didn’t occur to me until afterwards. The story has a surprisingly touching ending that reveals a bit about J’s own backstory and hints at more possible sequels. Now, if the follow-ups could only hold on to the franchise’s newly recovered mojo, I actually won’t mind if the agents’ silly, quirky escapade continues.