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A decidedly retro murder mystery is dressed up in very modern cinematic garb in this Swedish picture, which marries a rather old-fashioned serial-killer plot to corporate machinations and investigative journalism, and adds a brooding kick-ass punkette heroine to the mix. “The Girl With the Dragon Tattoo” is a heady brew, but a largely satisfying one.

The script, based on the first in a popular series of nouveau noir novels by Stieg Larsson, begins with reporter Mikael Blomkvist (Michael Nyqvist) being convicted of libel in his stories about a powerful industrialist and sentenced to jail—but not for six months. On leave with half a year on his hands, he reluctantly accepts an offer from reclusive businessman Henrik Vanger (Sven-Bertil Taube) to look into the decades-old presumed murder of his beloved niece Harriet. The girl disappeared from the family’s island compound in what amounts to a geographical “locked door” mystery, since her body was never found but the only bridge to the mainland was closed down on the day she vanished because of a terrible accident.

The mystery is compounded by the presence of so many relatives on the island on the fatal day, and by the family’s checkered history—which includes Nazi collaborators among Henrik’s dead or aged brothers. But Mikael’s efforts are further complicated by the intervention of another character—Lisbeth Salander (Noomi Rapace), the titular figure, a gloomy, black-garbed outcast who’s a legendary computer hacker and PI. The plot thread that introduces her shows her a no-nonsense pugilist when accosted by street thugs and a girl who embraces violent vengeance when she’s sexually abused by a sleazy legal guardian who demands favors in return for payouts from her trust fund (though unless I missed something, the source of the funds is never made clear).

The two lead characters link up when Lisbeth—for reasons that aren’t entirely clear, either—hacks into Mikael’s hard drive, and before long they’re collaborating in tracking down clues to Harriet’s disappearance. The clues, derived from the girl’s diary and finally shown to have some religious import, lead them to a series of brutal murders stretching back for decades, to interviews with witnesses and police officials and to the collection of reams of data from old newspapers and family photos. There’s opposition to their efforts from other members of the Vanger clan, some of which takes a very nasty turn. Eventually the truth is revealed, and it turns out to be dark, disturbing and shocking, and to involve some extremely ugly prospects for our hero and heroine. Rest assured, though, that as in most crime fiction the wicked are punished and the good (or perhaps less wicked) rewarded.

At its basis “The Girl With the Dragon Tattoo” is a murder mystery that Agatha Christie could have penned; the plot convolutions are frankly implausible, sifting through the detail can be exhausting, and the answers, when they come, certainly strain credulity. But director Niels Arden Oplev hides all that fairly successfully, not just by keeping things moving reasonably well but by reveling in the script’s opportunities for carnage. The most obvious examples are his protracted treatment of Lisbeth’s torture at the hands of her guardian (Peter Andersson) and her act of vengeance against him, and the final confrontation sequence between the unmasked killer and his pursuers. In fact, these scenes might prove too much for some viewers’ stomachs.

And the picture’s fascination is certainly enhanced by Rapace’s turn as Lisbeth, whom she makes a convincingly brooding, feral presence. Nyqvist is stuck with a significantly duller character, and he doesn’t manage to give him great vitality (or even intelligence, as it turns out). But the supporting cast is solid across the board. You have to give Andersson special credit for agreeing to undergo such gruesomely explicit humiliation. But the biggest surprise probably comes from the sweet, gentle air Taube brings to Henrik; it’s hard to believe this was the same fellow who played the lead agent so stiffly in the botched spy thriller “Puppet on a Chain” back in 1970.

Technically “The Girl With the Dragon Tattoo” is fine, with widescreen cinematography by Eric Kress that belies its origin as a television program and a sleek, subtle score by Blake Leyh. TV versions of the four later books in the Millennium” series have already been made, and two features assembled from them also cobbled together. This movie makes you look forward to seeing them, too.

Incidentally, the original Swedish title means “Men Who Hate Women.”