Andra Day and Kevin Hanchard in “The United States vs. Billie Holiday.” Takashi Seida/Paramount Pictures

Andra Day delivers an astonishing breakout performance as the complicated subject of “The United States vs. Billie Holiday,” in a movie that often feels like it’s unworthy of both the actress and the persona she adopts so seamlessly.

From the first moments of this maddeningly uneven film, Day channels her complicated, contradictory protagonist with closely observed detail. When a fey, feather-headed journalist asks her what it’s like “to be a colored woman” during a 1957 interview, she replies with a half-purr, half-snarl: “Would you ask Doris Day that question?” A few moments later, in a flashback to a performance 10 years earlier at the nightclub Cafe Society, Day delivers a rendition of “All of Me” with the physical glamour and eccentric but impeccably modulated musicality that made Holiday a star.

These are the moments that make “The United States vs. Billie Holiday” worth seeing, even if the choppy, episodic narrative that surrounds them is not just confounding but infuriating. A chronicle of Holiday’s harassment at the hands of Federal Bureau of Narcotics chief Harry Anslinger (Garrett Hedlund), the film is an intriguing addition to films that have tackled similar subjects recently, including “One Night in Miami,” “MLK/FBI” and “Judas and the Black Messiah.” In Holiday’s case, what was ostensibly an investigation aimed at her heroin use was really just a means of forcing her to stop singing “Strange Fruit,” the haunting ballad about lynching in the American South that became a civil rights anthem.

It’s a fascinating story and well worth revisiting. But in the hands of director Lee Daniels, working from a script by the playwright Suzan Lori Parks, what should be a sensitive and densely layered drama instead becomes a perfunctory collection of scenes that feel overwrought and under-considered simultaneously. A pageant of real-life characters traipse through the narrative: Tallulah Bankhead, Holiday’s friend and occasional lover, played with admirable restraint by Natasha Lyonne, shows up early and never returns; the long, ignominious line of men who beat and betrayed the singer becomes an indistinguishable pantheon of violent users and abusers; Jimmy Fletcher (Trevante Rhodes), the federal narcotics agent who infiltrated Holiday’s milieu, gets so close that he and Holiday fall in love.

Andra Day, left, and Trevante Rhodes in “The United States vs. Billie Holiday.” Takashi Seida/Paramount Pictures

That affair might be the most obvious flight of artistic imagination in “The United States vs. Billie Holiday,” which in building up that speculative romance manages to ignore Holiday’s far more interesting friendship and artistic collaboration with Lester “Prez” Young, played by Tyler James Williams in a literally thankless role. Alternately starchy and wildly over the top, the film demonstrates Daniels’s tendencies for both the literalistic and the lurid: If we’re not watching a stagy, Wiki-like biopic entry we’re plunged into the excesses of Holiday’s life at its most melodramatically bleak, whether in the form of a close-up on the needle going into her arm or her body being brutalized at the hands of one of her male tormentors.

Nowhere are Daniels’s elevated intentions more at odds with his baser cinematic instincts than in a druggy dream sequence, wherein Holiday revisits the abandonment and pain of her childhood, traumas that give way to the larger collective agony of an African American population living under the constant threat of white terror. The sequence is awkwardly staged and poorly edited, but it culminates in the most powerful moment of “The United States vs. Billie Holiday,” when Day sings “Strange Fruit” with spellbinding power and weary, regal, exquisitely calibrated fury. Viewers are left with the queasy feeling that we’ve been voyeurs to an exploitation of Holiday’s pain, but also, when Day gives her a chance simply to be, the beneficiaries of her genius.

“The United States vs. Billie Holiday” may not exactly win the battle for its embattled leading lady; but thanks to Day’s uncompromising performance, she somehow manages to win the war.