The riveting play “Between Riverside and Crazy,” which opened Monday night on Broadway, begins with a yuletide bait-and-switch: In one of the rooms of a sprawling apartment, we see a Christmas tree. 

But there are no carols, gifts and cocoa to match the mirth outside right now in Times Square, because Stephen Adly Guirgis’ dramedy is set during a New York summer. The characters, who live in Upper Manhattan, just haven’t bothered to lug their conifer out to the curb. It’s ho-ho-hot outside.

Having holiday decor lingering on Walt Spangler’s set during that stickiest of seasons unexpectedly says a lot about what will happen in this contentious household as the story unfolds. Some of the information the sharply written characters will admit, and that we accept without reservation, isn’t true.  

People we love become people we can’t trust, and back again.

As patriarch Walter, who is given a staggering performance by Stephen McKinley Henderson, resignedly says: “Who really knows anybody anyway, ya know?”  

Walter is a retired NYPD cop and a widower with an adult son named Junior (Common, in his Broadway debut). He lives with Junior and his friend Oswaldo (Victor Almanzar) in a massive, rent-controlled home on Riverside Drive that clearly isn’t cleaned much.

The former officer is both sweet and salty. Oswaldo and Junior are ex-convicts and still-generous Walter lets them live with him rent-free. But the man who everybody calls “dad” annoyedly waves off hugs and calls out peoples’ BS any chance he gets.

When his old partner Detective O’Connor (Elizabeth Canavan) comes over for dinner with her fiancé Lt. Caro (Michael Rispoli), an ambitious bigwig with the NYPD, details about Walter’s traumatic past are revealed and his very existence is threatened by those close to him.

Guirgis’ compassionate play, directed with great care by Austin Pendleton, is also wildly funny — actually more hilarious than many recent flat-out comedies — and devilishly inappropriate. His dialogue rightly doesn’t try to clean up how cops and convicts might talk and it also establishes that nobody here is a saint.

Common takes on his first major stage gig, successfully and admirably, in Broadway’s smallest house at just 597 seats and in a supporting role. Although the play isn’t Junior’s — it’s Walter’s — there’s complexity behind the rapper-actor’s warmth. He has a dicey past of his own and knows many of his father’s closely guarded secrets, but he always wants what’s best for dad. Junior navigating his touch-and-go relationship with girlfriend Lulu (Rosal Colón) is both affecting and kitty-corner to an episode of “Seinfeld.”

And Colón and Liza Colón-Zayas, as a church lady who visits Walter, are gifted comedic talents. Whoever thought holy communion and the word “prognosis” could be so funny?

However, it’s Henderson who shakes the stage. The wonderful actor, who’s been a regular for years in plays by August Wilson and Lorraine Hansberry and in films as far-removed as “Lady Bird” and “Dune,” gives the performance of his career and the Broadway season. 

He makes the complicated Walter a millions things at once — adorable, frightening, calculating, indifferent, reserved, commanding, a stand-up comic, a boozer — that combine into one indomitable theatrical force. It’s not the sort of showy, speechifying role that we usually laud out of habit. Often, Walter simply watches on. But as played by Henderson, he’s a man you won’t soon forget.