For “Argo,” Ben Affleck wears a dark beard that’s cut short but covers a lot of ground. He’s also grown out and conditioned his hair. It has body now. The movie finds a fresh angle into the Iran hostage crisis, which began in 1979 and lasted more than a year. That’s the right era for Affleck’s style. The beard looks like it placed third in a Son of Serpico contest. The hair could have come in second on Warren Beatty Night at the skate palace.

Setting aside intent, this doesn’t feel entirely accidental. Affleck plays a gentleman named Tony Mendez, a CIA operative with a specialty in hostage extraction. But any evocation of Beatty makes sense. Affleck directed “Argo,” and after a couple of Boston-steeped crime thrillers — “Gone Baby Gone” and “The Town” — his ambition for the thriller has gone international, it’s gone important, but, crucially, not self-important.

Affleck is the first actor since Beatty’s generation of stars to make a persuasive case for himself as an honest-to-goodness Hollywood filmmaker. He applies lightness but not too much. He’s serious but innocent of the pomposity that comes out of certain kinds of seriousness. If Affleck is trying to prove anything with this movie it’s that he’s egoless, empty of himself. He’s not making “Lions for Lambs.” He’s not, father forgive me, making “The Prince of Tides.” At least, he isn’t lighting himself that way.

“Argo” is set mostly in 1979 and 1980 Tehran, during the crisis, and focuses on the six US Embassy employees — played by Tate Donovan, Clea DuVall, Christopher Denham, Scoot McNairy, Rory Cochrane, and Kerry Bishé — who spent three months hiding out at the home of the Canadian ambassador (Victor Garber) and his wife (Page Leong), after Islamists overtook the embassy and held 52 Americans for over a year, demanding the US government return the overthrown Shah, Mohammad Reza Pahlavi, for trial (he died in Egypt in 1980). For Washington, the employees’ escape created a secret headache separate from the wider hostage situation itself. How to get these six out of Iran without getting them, the Canadians, or the 52 other Americans killed?

The film bolts between the CIA and Tehran until Mendez comes up with a solution. His plan for a clean exit out of Tehran involves a bogus film production, for which the embassy workers will pretend to be members of the crew, in town to scout shooting locations. The Washington scenes are full of the sort of actors you’d expect to find under these bureaucratic circumstances — Bryan Cranston, Chris Messina, Kyle Chandler, Titus Welliver — men who look good power-walking down hallways or asserting their skepticism at desks and conference tables, men who would have been bigger stars in the decades in which this movie’s set. Mendez receives the proverbial green light, flies to Los Angeles, and, with the help of a chummy makeup artist (John Goodman) and a producer — the crusty, bitter sort that only Alan Arkin can play — concocts an entire fake production. It’s a work of would-be sci-fi called “Argo,” and had it ever gone into production it might have starred Michael Ontkean or Harry Hamlin. Something like this actually happened. The Canadian government helped out with fake passports and was required, for reasons of diplomacy, to take credit for the whole thing. Poor Jimmy Carter couldn’t brag about it at all during his reelection campaign.