No fault with these stars. Running time: 165 minutes. Rated PG-13 (intense peril). Tuesday night at the Ziegfeld, the Lincoln Square IMAX, others.

Genius director Christopher Nolan reaches for the stars in “Interstellar” — and delivers a soulful, must-see masterpiece, one of the most exhilarating film experiences so far this century.

Astronauts Matthew McConaughey and Anne Hathaway journey to a distant galaxy on a desperate mission to save humanity in this brainy, heartfelt, gorgeous and flawlessly acted sci-fi epic — inspired by “2001: A Space Odyssey,’’ “Close Encounters of the Third Kind’’ and less likely sources such as “The Grapes of Wrath.’’

It’s the near future, 10 years after Earth began turning into a gigantic dust bowl, where those who don’t starve when crops wither soon face asphyxiation as nitrogen levels gradually rise in the atmosphere.

McConaughey is terrific as Coop, who’s retired from the space program and is a Midwestern corn farmer and widowed dad.

His feisty preteen daughter, Murph (Mackenzie Foy), is in trouble at school because she challenges a revisionist textbook claiming the moon landing was faked to justify “wasting’’ precious resources on the space program.

Coop and Murph soon learn that NASA has gone underground — and that his former mentor, Brand (Michael Caine), wants Coop to go back to work as the commander of a top-secret mission to save Earth’s population.

This requires traveling through a wormhole, a space shortcut beyond Jupiter that Brand believes has been placed there by intelligent life. It’s a wrenching sacrifice on Coop’s part — separating from an angry Murph and her brother for years.

By the time he’s reached his first stop in space, with Brand’s daughter Amelia (Hathaway), Coop has two decades’ worth of messages from Earth to play back — a killer scene.

The father-in-law (John Lithgow) who’s raised his kids has died, Coop’s son (Casey Affleck) is a father — and Murph has grown up to become a scientist (now played by a ferociously good Jessica Chastain) working for Brand, who fears Dad is lost in space.

I don’t want to give away too much, but the mission requires Coop and his crew to visit forbidding worlds with massive tidal waves and mountains of ice.

There’s also a witty talking robot (voiced by Bill Irwin), and a memorable encounter with a character played by an unbilled star who pretty much owns the movie for 20 minutes, including an almost unbearably suspenseful docking sequence.

The twisty plot by Nolan and his brother Jonathan also takes us on a mind-blowing trip inside a black hole that reminds us why the director of “Inception” is perhaps the most visionary director working today.

Nolan has a deserved reputation for emotionally chilly work, but “Interstellar’’ surprises with a Spielberg-like warmth — it’s basically a potent father-daughter love story at heart, even as the filmmaker explores “bigger” themes like the survival instinct and American exceptionalism.

At a time when large-scale filmmaking consists pretty much of movies inspired by comic books, young-adult novels and the Bible, Nolan still makes wholly original movies that require audiences to pay close attention and think.

You may have heard that “Interstellar’’ has a lot of exposition, including what amounts to a crash course on physics.

True, but you’ll be rewarded with a sublime trip to the movies if you go with the time-space flow. Bring lots of tissues.