That odor coming from the Guthrie proscenium theater? “That’s the powerful smell of mendacity,” as Big Daddy would have said to Brick, in Tennessee Williams’ “Cat on a Hot Tin Roof.”

Playwright Jon Robin Baitz has created another powerful family clinging to its legacy in “Other Desert Cities.”

The privileged Wyeths, ensconced in the baked and bland confines of Palm Springs, are struggling with the consequences of lies, tragedy, politics, the corrosive power of secrets and the slippery perceptions of truth — all on the night before Christmas. Oh, unholy night.

Baitz’s crackling serio-comedy, which opened Friday at the Guthrie, probes painfully into the aching heart of the Wyeth’s personal tragedy. Daughter Brooke (Kelly McAndrew) arrives from the east coast and plunks down the manuscript of her new memoir — a sort of early Christmas present for her parents, Lyman (David Anthony Brinkley) and Polly (Sally Wingert.)

Unsteadily, Brooke says the memoir deals with her older brother, Henry, whose leftist rebellion and suicide devastated the family. Writing has exorcised a depressive demon in her, she says with a slight sense of her own importance.

Lyman and Polly are remnants of the Hollywood Republican tribe. A former actor, Lyman became party chairman and learned compromise and congeniality at the feet of his friend, Ronald Reagan. Brinkley conveys him with a charming smile, a warm heart and a thundering sense of his own accomplishment. Polly, who once wrote screenplays, puts her steel spine and feral ambition to raising money for the party and declaiming on how drugs and irresponsibility nearly ruined the country in the 1970s. Wingert gives a ferocious portrait of icy resolve. Chided by her son that in the end of life, all that matters is love — so why can’t she just love — Wingert’s Polly says, with scorching self-awareness, “I can’t. I’m not built for it.”

So when Brooke announces that she has exhumed Henry’s memory in her soon-to-be-published book, mom and dad are threatened.

Son Trip (Christian Conn), who produces reality TV shows, allows his sister her artistic freedom, but says she is naïve if she thinks there will not be consequences.

The fifth wheel on this vehicle roaring into the searing desert heat is Silda (Michelle Barber), Polly’s sister, who only recently has denied her acid tongue the taste of booze. Silda’s scratchy cyncism punctures the tension with bons mots, but she too lives with mendacious secrets.

Baitz’s great feat in the script is his refusal to take sides. Just when one combatant has triumphed, the foe rises like a Phoenix with a counter punch. Baitz finds resolution less interesting than a multiplicity of motivations, psychologies and ideas. This makes for delicious revelations, particularly in the second act when, after the sun goes down and the desert chill comes up, the Wyeths can release their inner vampires.

Director Peter Rothstein’s production comes out of the gate a little hot and it’s not until Barber’s Silda appears midway through the first act that the flow becomes organic. McAndrews, in particular, shows us that she’s acting at key moments rather than slipping into the hide of a fully understood character. James Youmans has created a set of stones, teakwood and beige on beige that exhales arid desert air.

Just as in the plays of Williams, Inge, Miller, Albee and O’Neill, Baitz has found in the permeable and permanent hooks of family a play that questions our own mythologies, rivalries, personal and collective needs. This is a show worth seeing again and again.

Graydon Royce • 612-673-7299 • Follow on Twitter: @GraydonRoyce