In his new film “The Adjustment Bureau,” Matt Damon’s driven, iron-bodied character bursts into a crowded New York cafe with fire in his eyes and an urgent plea.

“Excuse me!” he shouts over the din, as alarmed diners put down their forks for what is surely a matter of life or death. “Has anyone here seen a performance at Cedar Lake Ballet Company?”

He’s asking this because, at this particularly heated point in the plot, there is nothing more important than finding this little out-of-the-way dance troupe.

His future, his fate — everything rests on it. Sounds silly, perhaps, but the beauty of this film is how it fits dance, the most ephemeral and fragile of the arts, so seamlessly — and even poetically — into a muscular action flick. Dance fans, rejoice: If you were among those guffawing through the implausibilities of “Black Swan,” if you have despaired of Hollywood ever losing its adolescent view of dancers, “The Adjustment Bureau” is a film to lift your spirits. Dance is handled extraordinarily well in this treatise on fate versus free will, in which a grim cabal of secretive hat-wearing men stalks Damon, as rising politician David Norris, to keep him on his preordained path — whether he likes it or not. (He doesn’t.)

“The Adjustment Bureau” is not, by any means, a dance film. But woven through the chase scenes and the romance is the quest for freedom, to do what you want and love whom you wish. Destiny dukes it out with serendipity. And in the crucial role of David’s aha! moment: a dancer. His love interest, Elise — who is also the reason the Adjustment Bureau suits are on his tail — is played by Emily Blunt in one of the most believable actor-portrayals of a dancer in recent memory.

What Blunt captures — and what the script, by writer-director George Nolfi, movingly underscores — is the elevating, liberating power of dance. Blunt’s Elise is a bright, independent free spirit who unlocks something vital in Damon’s dutiful, over-managed do-gooder. She’s the intellectual equal of the aspiring senator, and as she teases him for eyeing her legs or dunks his BlackBerry in his coffee, she brings out the charismatic friskiness that he has submerged for the campaign. When he spies on her rehearsal at the ballet studio — after one of those cafe patrons whose lunch he has interrupted volunteers the address — Elise shows him a world of self-discovery and beauty.

“If he sees her dance, it’s over,” one of the bad guys warns another. You can see why they fear her influence as David falls under the sway of Elise’s solo, shown ever so briefly — and tantalizingly — as an expression of questioning, and the emergence from dark into light.

This is why a dancer’s influence, her desire to push and explore on a level beyond words, is so dangerous to the men who seek to control David. The Bureau — representing Fate, or maybe a none-too-benevolent God or the higher power of your choice — can’t deal with freedom. At one point, one of the Bureau agents confides to David: “Improvisation — we have trouble with that.” (I choose to see that as a dance reference, too.)

For its heroic view of dance, for presenting the art form the way we who love it see it, I am willing to overlook the fairy-tale aspects of the film, its magical, Harry Potter alternate reality of secret doors and enchanted talismans. (We learn the reason for the hats, and it’s a disappointment.) Even with the hocus-pocus, this movie has my allegiance — and not only for its well-considered view of dance. It also presents a healthy and realistic image of a dancer, inside and out.

From the moment you see Blunt, slipping out of a men’s bathroom stall at the Waldorf Astoria where she’d been hiding (a screwball entrance that she carries off with iron dignity, the way a disciplined stage performer would), she looks like a dancer. It’s all in her upright carriage and the openness across the chest — and I’m not referring to the impressive plunge of her party dress, but to the bearing of her upper body, her broad shoulders and athletic, sculpted arms.

Imaginatively edited shots of her dancing, mostly being lifted and tossed from one male dancer to another, bring about exactly the feeling of freedom and flight that is one of dance’s most glorious payoffs. Most of all, Blunt’s Elise is sharp and grounded, with a no-nonsense directness that feels absolutely right for a contemporary dancer. These are, after all, among the Western world’s great survivors, scratching out a living in urban centers, subsisting on Advil and salad, navigating a tricky matrix of rent payments/health coverage/unemployment insurance, hoping good health and luck will help them cheat their own encroaching fates.

Blunt, who had no previous dance experience, trained for her part with the real Cedar Lake Contemporary Ballet, a 16-member troupe in Chelsea led by Benoit-Swan Pouffer, a former dancer with Alvin Ailey American Dance Theater. According to a company spokesman, Nolfi chanced upon a performance, became a fan and decided its freewheeling street-earthiness was just right as a counterbalance to David’s buttoned-up conservatism. (The script is based on Philip K. Dick’s short story “Adjustment Team,” though Nolfi tinkered with the plot and characters.) Yet though Blunt spent several weeks taking classes with Cedar Lake, she relies mostly on artful acting to convey a dancer’s outlook and physicality.

At one point, in one of those magical plot twists, she bursts through a door and into Yankee Stadium; in sheer wonderment, Blunt veers away from Damon and into the open space in a subtle dance move, as if she’s instinctively drawn to what is, in effect, a very big green stage.

It’s no surprise that Damon also imbues his character with an astute physicality: You could think of David as a cousin to Damon’s Jason Bourne roles, an idealistic Everyman who is every bit as adrenaline-fueled as the amnesiac assassin. But when, at one point, he makes a soul-killing choice to follow the Bureau’s plan, the shambling, old-man gait with which he ends the scene says what he can’t bear to speak aloud.

“The Adjustment Bureau” isn’t anchored in reality, and perhaps to emphasize this, there are anachronistic touches throughout. With their gentlemen’s hats, the Bureau men are slightly out of time; their head agent, known only as Thompson (Terence Stamp), has a stuffy, Dickensian look in his three-piece suit and silk scarf. But there’s another bit of nostalgia thrown in, a sweet one — unintentionally so, I suspect. That’s the proposition that an unknown dancer from a niche downtown troupe could one day hope to become world-famous and, beyond that, go on to global adulation as one of the greatest choreographers ever, which — at the risk of giving too much away — is the cosmic plan that the Bureau has in mind for Elise.

In other words, she could ascend to the heights of Martha Graham, Paul Taylor or Mark Morris, a path along which no one has trod in recent years, as funding has dwindled and audiences grow more conservative and more choosy. But it’s a lovely thought — and a view of a world I was grateful to inhabit, if only for a couple of hours.