J.J. Abrams might not have been able to revivify Tom Cruise’s “Mission Impossible” series, but he works wonders with Gene Roddenberry’s forty-year old space franchise, which has been in the doldrums for a while. “Star Trek” is a fast-paced, witty prequel to the sixties show, a top-flight modern adventure that even the most die-hard, protective Trekkers will swoon over. (See, I know enough not to say Trekkies.)

In that respect it’s miles ahead of the first “Star Trek” movie, Robert Wise’s turgid 1979 yawner that featured the original television cast and nearly killed the golden goose. 1982’s “The Wrath of Khan” rescued matters, but through the eighties and nineties the series settled into a benign mediocrity on both the big screen and the small one, until as the century turned it reached a nadir with “Nemesis” on the one hand and “Enterprise” on the other.

That’s why it’s a pleasure to report that Abrams and his cohorts have managed the near-impossible—fashioning a picture that’s not only an affectionate tribute to the original show but a successful rebooting of the whole franchise, which promises to take it into uncharted territory rather than merely repeating what’s gone before and plugging in holes along the way. The only thing it really lacks is the sort of humanistic message that was always built into the old shows and films; it’s not preachy in the way they usually were, going for sheer visceral punch and even closing with a big celebratory medal-pinning moment that can’t help but recall the close of the first “Star Wars.” But in these times the lack of a heavy-handed moral is probably a virtue.

The solution of writers Roberto Orci and Alex Kurtzman is to go back beyond the beginning, as it were, briefly but skillfully sketching Kirk and Spock’s childhoods—emotionally difficult in very different ways—before depositing them both at Star Fleet Academy in the persons of Chris Pine and Zachary Quinto, where they aren’t exactly natural friends. They wind up together aboard the fleet’s new ship, the Enterprise, commanded by Christopher Pike (Bruce Greenwood), in response to a distress call from Vulcan. And along for the ride are the young Uhura (Zoe Saldana), “Bones” McCoy (Karl Urban), Sulu (John Cho) and Chekov (Anton Yelchin).

The mission brings them all into battle against Captain Nero (Eric Bana), a renegade Romulan out for vengeance against the Federation and equipped with a massive ship that boasts technology that’s literally futuristic and capable of destroying not just starships but whole planets. After Pike’s taken hostage by him, Kirk and Spock joust over the proper way to proceed and Kirk winds up on a barren ice planet where he encounters not only master technician Scotty (Simon Pegg) but the older, wiser Spock (Leonard Nimoy), who effectively explains the plot to us via mind-meld.

To be honest, the procedure works better with young Kirk than it does with the audience; at least for this viewer—admittedly not a particular devotee of the previous franchise incarnations—all the discussions of time warps, black holes, red matter and the like are pretty impenetrable. But it doesn’t really matter, because Abrams keeps things percolating so excitingly that the action scenes and great effects will grab you even if you’re not entirely clear about why things are happening as they do. The prologue—in which Kirk’s father meets an untimely demise at Nero’s hand—is a smashing opening, and later there’s an exhilarating parachute drop by Kirk and Sulu onto a huge space drill, followed by an equally fine fight scene involving them and two fearsome Romulans. And the final act is a doozy, although one might question Kirk’s sojourn on that ice planet, which not only features an encounter with a creature that’s frankly the worst CGI idea in the picture but derives from a decision by Spock that’s not just illogical but frankly despicable.

Still, it does bring in Nimoy, who anchors the picture just as Alec Guinness did “Star Wars,” bringing a gravitas to the story that balances beautifully against the higher spirits of the younger actors. And against all odds they’re uniformly fine, channeling the old cast and toying with echoes of the characters’ established personas (Bones’s gruffness, Sulu’s swordplay, Spock’s catch-phrases, Chekov’s accent) without sending them up. Pine makes a stalwart hero, less stiff than the young Shatner was, and Quinto is just as good as a Spock who’s not yet fully mastered his human side. Urban, Saldana and Cho are all strong, and Pegg—who one might have feared would go too far over the top—adds humor without too much mugging. But the standout might be Yelchin, who gives Chekov an ebullience that’s infectious.

Among the others Bana is a solid villain—he brings a lot of Ricardo Montalban’s Khan to Nero—and Greenwood makes a stern but avuncular Pike. The supporting players deliver down the line, with Ben Cross and Winona Ryder (of all people) fine as Spock’s parents and Chris Hemsworth and Jennifer Morrison equally good as Kirk’s. And they’re all set within a solid technical production courtesy of designer Scott Chambliss and art director Keith P. Cunningham, set off by expert camerawork by Dan Mindel and sharp editing by Mary Jo Markey and Maryann Brandon, which helps the picture to actually seem shorter than it is. Even the costumes—discreetly updated by Michael Kaplan—are a plus. Only Michael Giacchino’s score seems a mite too bombastic.

But the success of Abrams’s “Star Trek” really goes beyond this movie, which remains essentially true to the wide-eyed spirit of Roddenberry’s vision while excising the geeky quality that clung to later installments of the series. The way it ends—with the young versions of the familiar characters facing a changed universe from the one their former incarnations did—can help insure that future additions won’t be mere remembrances of times past but genuinely new adventures with unexpected twists and turns. I think it’s fair to say there will be plenty of them, and if they maintain the quality of this initial outing, they’ll be voyages well worth taking.