In the opening scene of “The Killing of a Lesbian Bookie,” burlesque star Triple Lexxx is meeting with a liquor distributor, Irish, who has stopped by her apartment to discuss beer selections for her soon-to-open nightclub.

Irish is drawn to Lexxx’s extensive collection of classic movies, and one in particular catches his attention: John Cassavetes’ 1976 crime drama “The Killing of a Chinese Bookie.”

“I think it’s a movie about people who just can’t help themselves,” says Lexxx, honing in on a theme repeated throughout the play, making it clear that the show’s characters resemble this remark.

Written and directed by Jim Fitzmorris (“Be a New Orleanian,” “A Truckload of Ink”), “The Killing of a Lesbian Bookie,” running through July 3 at The Theatre at St. Claude, is a pitch-perfect homage to the gritty American crime films of the 1970s, and the play is rife with references to classics of the genre, from “Chinatown” to “The Godfather.”

While there are no car chases, seedy nightclub scenes, or big burlesque numbers, “The Killing of a Lesbian Bookie” latches on to the cat-and-mouse games between bad guys and badder guys that define the films that inspired the play.

Lexxx, played by New Orleans burlesque performer Bunny Love, talks up the art of the “slow reveal,” which is both an essential element of striptease and a driving force of the play.

The playful, coy banter between Lexxx and Irish (Justin Welborn, whom audiences might recognize from his recurring role on the FX series “Justified”) eventually unfolds into a complicated plot that includes crooked cops, Hollywood starlets, organized crime bosses, and corrupt government officials.

In the “reveal” that follows the “slow,” Lexxx’s lover — the lesbian bookie of the play’s title, played by Kimberly Kaye — returns to the apartment and the action turns taut, as the three characters are forced to untangle their fates and fend for themselves.

Fitzmorris’ script effectively captures the dark drama of the genre, creating characters that are unsympathetic in their cold calculations, but who become more and more intriguing as the story plays out. His direction is sharp, keeping the characters confined to the small apartment, but rarely letting them sit still.

Love and Kaye turn in fine performances. Love is particularly effective when Lexxx gets caught between Irish and the bookie, her allegiances torn.

Welborn commands the stage as Irish, never leaving any doubt as to who is really in charge of the characters’ volatile predicament.

David Raphel’s set design is impressively polished in its realistic approach to the play’s apartment setting.

Costume designer Dana Marie Embree gets a big reveal of her own at the tail end of the play, briefly showcasing the glitz and glam one might expect from a story about a burlesque dancer on the verge of opening the hippest, sexiest club in town, but otherwise the production opts for low-key cool.

Since Fitzmorris, along with his brother Ryan, assumed management of The Theatre at St. Claude last summer, the venue has hosted or produced a number of shows, staged readings, and other events, but “The Killing of a Lesbian Bookie” is the first fully realized show from Broken Habit Productions, the theater’s resident company.

With more full productions scheduled for later this year, “The Killing of a Lesbian Bookie” is another step forward in establishing The Theater at St. Claude as a destination for exciting, innovative theater in New Orleans.