Tana Hicken as Vera and Grant Harrison as Leo in the production 4000 Miles at Studio Theatre; photo by Teddy Wolff. (Teddy Wolff)

Playwright Amy Herzog has arrived in a hurry. First New York: she has conquered off-Broadway with three acclaimed productions in the past 12 months, starting with the Lincoln Center Theater’s extension of “4000 Miles,” her poignant drama about a grieving 21-year-old hippie and his 91-year-old communist grandmother.

Now it’s Washington’s turn. “4000 Miles” has opened in a new staging at Studio Theatre, which led The Post’s Peter Marks to call Herzog “a playwright of distinction” and the play “smart and penetrating.” In September, Theater J will offer “After the Revolution”; like “4000 Miles,” it’s based on Herzog’s family, but it takes a sharper look at the clan’s intense leftist politics.

The praise for Herzog’s emergence has been striking. “No one currently writing for the theater has a sharper grasp of character, or more sheer storytelling technique,” Time magazine declared last month.

That was on the occasion of “Belleville,” an unexpected thriller about a young American couple falling apart in Paris. (Its near-sellout run ends Sunday at New York Theatre Workshop.) That followed the recent extended engagement at Playwrights Horizons of “The Great God Pan,” in which a man grapples with the sudden suggestion that he was sexually abused as a child.

Amid this flurry, Herzog, 34, pinpoints the move of “4000 Miles” from a small 42nd Street space to the Lincoln Center as the breakthrough moment.

Amy Herzog (Courtesy Amy Herzog)

“It was suddenly a really big jump careerwise,” Herzog says by phone from her home in Brooklyn.

She is married to the in-demand director Sam Gold (the couple has an 11-month-old daughter). They choose not to work together professionally, which is an interesting line to draw, given that Herzog often blurs the boundaries between art and actual family history.

The overlap is so pronounced that last spring the New York Times interviewed Herzog with her grandmother, Leepee Joseph, who was then 95. Leepee Joseph was the blatant basis for the grandmother, her name slightly altered to Vera Joseph, in both “After the Revolution” and the subsequent “4000 Miles.”

Herzog’s biographical data is all over “4000 Miles,” from the fervent 1940s-1950s communism still espoused by Vera to the cross-country bike trip that Vera’s grandson Leo unexpectedly finishes at her Manhattan apartment in the middle of the night. Herzog once braved such a ride herself, and the bike that appeared onstage in the New York production was hers.

“After the Revolution” is even more saturated with Herzog’s family drama. The play concerns a bright young woman poised to carry her well-known family’s proud liberal torch, until she learns that her grandfather was not merely an American socialist but a Soviet spy.

It’s true: Herzog’s real grandfather passed secrets to the reds. (For details, Google the Venona project, which became public knowledge in the 1990s.)

“That caused some major ripples in my family,” Herzog says. “It only occurred to me later, maybe 2006 or 2007, that there might be a play in it. I had an inchoate sense of disappointment, or maybe embarrassment, that I had this pride that had gone unexamined.”

She speaks rapidly — “inchoate” is just part of the flow — and clearly thinks fast. Her characters are quick, too, even if her plays don’t seem to be in much of a plot-driven rush. Joy Zinoman, Studio’s founding artistic director, has come out of her recent retirement to direct “4000 Miles,” and she talks about Herzog’s subtle storytelling, her crafty touch with exposition.

“I’m in heaven,” Zinoman says, describing the delicacy and depth of the play’s situations and people. How carefully calibrated is it? Several key figures in the 90-minute play — a neighbor, a sister, a mother, a friend — are never even seen. The four characters we do see — the grandmother, the grandson, a girlfriend, a hookup — are engrossingly complicated.

Herzog can cite playwrights she admires from Kenneth Lonergan and Craig Lucas to Chekhov and Ibsen. But she believes novels and short stories have been a bigger influence on her writing.

“A lot of plays feel a responsibility to plot that novels don’t, because you can take your time with a novel,” Herzog says. “I try to write really interesting characters instead of riveting plots.”

She majored in English — “I was always more passionate about literature than anything else” — before grad studies in playwriting at Yale. She acted after graduating, but not for long.

“When I failed at acting, I stopped acting,” she says. “When I failed at writing, I kept writing.”

“After the Revolution,” is her only political play but an unusual political fluency percolates through all the works. In “4000 Miles,” a young Chinese American woman takes issue with the communist books in Vera Joseph’s apartment. In “The Great God Pan,” a character mentions single-payer health care briefly, yet seriously.

“I am obsessed about the politics of health care in this country,” Herzog says. She tells a story about buying medicine for her daughter; insurance didn’t cover it because an ingredient was water.

“I’m completely amazed by strange Kafkaesque world of health care that we all live and die by,” she says. “I’ve been thinking there could be a great farce. But I don’t know if I’m the right writer for it.”

Herzog hardly claims the mantle of political playwright, given her idiosyncratic focus on “the old hard-line reds” she grew up knowing in her extended family. (Her ongoing theme, she says, is “well-meaning people failing each other, and living with that failure.”) She casts a writer’s critical eye at the vintage socialist values, yet remains bound by her blood connections.

At least that’s how it looked last week as Herzog, slender and simply dressed in blue jeans and a thin green sweater, attended a performance of “4000 Miles” at Studio. She didn’t cancel the D.C. date even though her grandmother, Leepee Joseph, had passed away that morning at 96.

“This whole thing was about her,” Herzog explained afterward during a quiet moment backstage.

Hollywood already knows Herzog; she’s working on a romantic comedy screenplay for Castle Rock. She has no more plays in the chute. Writing two or three in the next five years would be nice.

“I wrote four plays in the last five years, but I don’t expect to be that productive ever again,” Herzog says. Professionally, her goals have been met: “Just to be a playwright, and to have productions I could be proud of off-Broadway. I don’t feel that there’s anything missing.”

4000 Miles

by Amy Herzog. Through May 5at the Studio Theatre, 1501 14th St. NW. Call 202-332-3300 or visit www.studiotheatre.org.