President Lyndon Baines Johnson was bigger than life, brimming with contradictions, filled with passion yet not above petty politics.

Only a great actor should even attempt to portray such a complicated, historically significant figure — and after seeing HBO’s “All the Way,” I’m convinced few if any actors on the planet could match the singularly talented Bryan Cranston’s portrayal of LBJ.

Director Jay Roach (who helmed the Cranston-starring “Trumbo,” as well as the “Austin Powers” movies) turns Robert Schenkkan’s acclaimed Broadway play into an engrossing, powerful if slightly overcrowded movie that works as a biopic of LBJ and as a time capsule of a crucial period in the civil rights movement.

Cranston’s performance in the stage version won the Tony for best actor. They might as well engrave the Emmy with his name right now.

“All the Way” begins on one of the saddest moments in American history: the assassination of JFK in Dallas on Nov. 22, 1963. On Air Force One on the flight back to Washington, now-president LBJ shares a quiet moment with his wife Lady Bird (an almost unrecognizable and very strong Melissa Leo) — but then complains to his wife about the way Jackie Kennedy was looking at him during the swearing-in on the plane.

It’s a glimpse into the complex inner workings of LBJ. Although he and the Kennedy brothers were often mortal enemies, he felt genuine grief over the loss of a young president — but he still had room to nurse his wounded ego over the perceived resentment of a woman whose husband had just been murdered so close to her that her dress was spattered with his blood.

The first half of “All the Way” concentrates on Johnson’s yeoman effort to pass a Civil Rights Act without permanently alienating Dixie Democrats and destroying his chances for election in 1964.

Every time a new historical figure applauds an LBJ speech or enters the Oval Office or appears at a civil rights meeting, we get helpful graphics identifying some of the major players of the time, including:

• Anthony Mackie as the Rev. Martin Luther King Jr.

• Frank Langella as Sen. Richard Russell, an old-school, anti-reform Southerner who was more of a father figure to LBJ than LBJ’s own father.

• Steven Root as FBI director J. Edgar Hoover, who was obsessed with spying on King and revealing his extramarital affairs.

• Bradley Whitford as Minnesota’s Hubert H. Humphrey, a passionate advocate for civil rights who became LBJ’s vice-president and remained loyal to the president even when LBJ was roaring insults to his face.

Mackie doesn’t try to impersonate King, but he does a fine job of capturing King’s struggle to navigate the political waters of Washington D.C. while growing increasingly frustrated with broken promises and stalled negotiations. Langella is the perfect choice to play the intimidating and stubborn Russell. Root is oily and effective as the creepy but inarguably influential J. Edgar Hoover.

Best of all the supporting work: Whitford as Humphrey. Whitford captures Humphrey’s look, mannerisms and catchy speech patterns — and more important, he shows us the man’s integrity, his decency and his willingness to take LBJ’s crap if it means striking another blow against bigotry. It’s a wonderfully realized performance.

The second half of “All the Way” isn’t quite as effective as hour one, in part because Roach and Schenkkan are perhaps too ambitious in addressing touchstone moments in LBJ’s presidency, from the Gulf of Tonkin to a sex scandal involving one of his most loyal aides to the murders of three civil rights workers in Mississippi to the infamous and controversial anti-Goldwater “daisy” TV ad.

But even when “All the Way” takes a slight wrong turn or stalls a bit, it looks and feels authentic, from the use of newsreel footage — staunch segregationist George Wallace is not portrayed by an actor and appears only in black-and-white clips — to the sets, to the incredible makeup work that helps immeasurably in the process by which Bryan Cranston disappears and Lyndon Baines Johnson commands our attention.

★★★1⁄2

HBO Films presents a film directed by Jay Roach and written by Robert Schenkkan, based on his play. Running time: 130 minutes. Premieres at 7 p.m. Saturday on HBO.