NEW YORK — For a heart-piercing ride-along on the avalanche of emotion engulfing the parent of a desperately ill, incapacitated child, playwright Amy Herzog exceeds her own fine record of accomplishment with “Mary Jane.” The gifted author of “4000 miles” once again tallies the joys and sorrows that family ties engender. Only this time, it is a force beyond human control at the root of a woman’s wrenching daily regimen, a situation that allows us to understand what happens to a family when nature goes awry.

Or rather, what occurs after technology has intervened, making possible life where it otherwise probably wouldn’t, and leaving a single mother to struggle with the consequences. Carrie Coon (of TV’s “Fargo”) plays that mother smashingly in New York Theatre Workshop’s impeccable production, flawlessly directed by Anne Kauffman, that had its official off-Broadway opening Monday night.

Coon’s Mary Jane, living with an almost 3-year-old son born at 25 weeks and now surviving with the help of round-the-clock nurses and feeding machines, has had to sacrifice almost everything else in her life to care for Alex: career, mate, financial security. One of the marvels of “Mary Jane” is that the mom carries on with an almost superhuman cheerfulness. It is the play’s admirable conceit that Mary Jane’s stubborn optimism — a fortitude of an almost holy magnitude — is simply a fact of her life. Mary Jane has been dealt a difficult hand, but cushioned by her love for Alex, she finds meaning, even a kind of solace, in putting up a fight for her boy, at home and in the hospital.

The 100-minute play introduces us to Mary Jane at a crucial juncture in her struggle to keep Alex alive in their modest New York apartment with the help of a nurse, Sherry. Played by the affecting Liza Colon-Zayas, Sherry evinces that saintly sort of fierceness you pray would materialize in your life should you need someone to watch over you. Along the way, we meet two disparate mothers with children in similar kinds of limitless distress, both played poignantly, and amusingly, by the superb Susan Pourfar: some people, it seems, can accept the terms of this daily excruciating battle; others seem defeated just as it gets started.

Herzog invests in each of her characters — the others are played with disarming clarity by Danaya Esperanza and Brenda Wehle — a beguiling sense of authenticity. After the drama shifts to a hospital’s pediatric intensive-care unit, that cold-eyed impression of truth awakens an audience to a larger reality, the fight going on at the national level, over health-care insurance in America, and who has access to its benefits. You’re compelled to wonder what horrors Mary Jane and Alex might have faced, if they’d had Mary Jane’s strength, and that alone, to see them through.

Mary Jane, by Amy Herzog. Directed by Anne Kauffman. Set, Laura Jellinek; costumes, Emily Rebholz; lighting, Japhy Weideman; sound, Leah Gelpe; stage manager, Lisa Ann Chernoff. About 100 minutes. $69. Through Oct. 15 at New York Theatre Workshop, 79 E. 4th St., New York. Call 212-460-5475 or visit