(L to R): Denisha Ballew as Serena, Alicia Hall Moran as Bess and Kingsley Leggs as Sporting Life in The Gershwins’ “Porgy and Bess.” (Michael J. Lutch)

It drives Diane Paulus nuts, seeing people asleep in their theater seats. Not because she considers it a breach of playgoing etiquette. No, the torture for this Tony-winning director is the possibility that what’s happening onstage is of such marginal interest that it works on some portion of the audience as a sedative.

“You never see a person sleeping at a sporting event!” she said the other day, as she munched on a cheeseburger in a Times Square restaurant. “I mean, what are we doing wrong if people feel more engaged at home with their laptops?”

It’s worries of this nature that Paulus bundled up five years ago and carried with her to Cambridge, Mass., to take over the leadership of the American Repertory Theater, a respected if not inordinately high-profile company affiliated with Harvard University and founded by critic and director Robert Brustein.

And wouldn’t you know: Wake up the organization she did, initiating and importing a slew of projects that have propelled ART from estimable regional purveyor and into the ranks of the most exciting outlets in the nation for musicals and plays both new and reconsidered.

One of ART’s reinterpreted classics, a revival of “Porgy and Bess” that was retitled “The Gershwins’ Porgy and Bess,” makes its way to Washington’s National Theatre this week, on a national tour spawned by the production’s Tony-winning, 293-performance run on Broadway. (The show, which starred Audra McDonald, Norm Lewis and David Alan Grier, won the best musical-revival statuette in 2012 over, among others, the Kennedy Center’s “Follies”; the cast of the road company is headed by Alicia Hall Moran as Bess, Nathaniel Stampley as Porgy and Kingsley Leggs as Sporting Life.)

“Porgy and Bess” has historic ties to Washington. In 1936, the cast of a touring production, led by Todd Duncan as Porgy, forced the National to allow the opera to be seen by an integrated audience.

The current production leapt onto Broadway from ART’s home base, the 540-seat Loeb Drama Center, as one of an astonishing string of critical and/or popular hits that the 47-year-old Paulus has sent into the world. The revival of “Pippin” that won the Tony for best musical revival in June (and one as best director of a musical for Paulus) is doing boffo box office on Broadway, as is the revival of Tennessee Williams’s “The Glass Menagerie,” directed by John Tiffany and starring Cherry Jones and Zachary Quinto, that debuted at the Loeb last season.

Once,” which won the 2012 Tony for best original musical, had its premiere a year earlier in Paulus’s theater, and “Sleep No More,” the wildly successful interactive mystery that requires ticket holders to follow actors randomly around the rooms of a house, had its first American toehold courtesy of a run at ART. This is not to mention “All the Way,” a new drama by Robert Schenkkan about President Lyndon B. Johnson and his drive to get passed the 1964 Civil Rights Act. It comes to Broadway in the spring, following a sold-out engagement in Cambridge, with none other than “Breaking Bad’s” Bryan Cranston as LBJ.

It is hard to come up with another American company whose creative footprint at the moment is making such a deep impression on the country’s theater. And if this turn of events is traceable to ART’s artistic director and her sixth sense for what keeps audiences alert — and happy — one must ask: Why aren’t other companies doing more to emulate her? ART certainly seems eager to keep her on track: She just re-upped with the institution for another five-year term.

“I was watching her from afar,” said William Russo, recently hired as ART’s managing director, after a long career at such off-Broadway mainstays as Playwrights Horizons and New York Theatre Workshop. Of all the incentives to take the job, he said by telephone from Cambridge, Paulus was “the major draw. I saw just how quickly she started to put her stamp on the theater. She said, ‘There’s something I want to do here.’ ”

And he appreciated that her philosophy was so focused on understanding the kind of experiences that audiences desire. “I loved when she said to me, in her mind, the theater has to be about more than the two hours you sit in the dark.”

Paulus, who has her undergraduate degree from Harvard and later took acting classes from director Mike Nichols, emerged as an off-Broadway director in the 1990s, with offbeat ventures such as “Running Man,” a jazz-inflected chamber musical that in 1999 was a finalist for the Pulitzer Prize for drama. Her ascendancy really began, though, with another off-Broadway production that same year: “The Donkey Show,” a version of “A Midsummer Night’s Dream” set in a disco. At a time when “interactive” in the theater meant schmoozing over pasta with other “guests” at “Tony ’n’ Tina’s Wedding,” Paulus and co-creator (and husband) Randy Weiner took a wittier path, in trying to make a party of the thematic common ground that could be shared by Shakespeare and Summer — Donna Summer, that is.

“The Donkey Show” stamped Paulus as a director who could meet audiences at the seductive juncture of highbrow and low. All these years later, the piece is a fixture at Paulus’s ART, where it’s performed on Saturdays in the Oberon, the group’s second stage. Over time, you can see how the idea of giving audiences a variety of opportunities for intimate encounters with the work has been a Paulus hallmark. In her revival of “Hair,” first staged for the Public Theater in Central Park in 2008 — and later another Tony-winning revival for her — she invited the audience onto the stage at evening’s end, for a nightly, dancing be-in.

“The world changed, but I don’t think the art was reflecting the world we live in,” Paulus said, invoking her thesis that theater is becoming an ever more elitist pastime, that there has grown among some in the theater community a belief that art that is popular isn’t as worthy. That is not to say that Paulus only goes in for entertainments like “Pippin,” whose carnival atmosphere she’s pumped up, to Cirque-du-Soleil-style proportions. The project with which she’s currently in rehearsal in New York, “Witness Uganda,” is a new musical about American aid workers that begins performances at ART on Feb. 4. And no, she says, the impression of that African nation will bear zero resemblance to the Uganda lampooned in “The Book of Mormon.”

Still, her leadership model remains a work in progress: In spite of all the Broadway transfers, for instance, ART and its $14 million budget remain a break-even operation, with the royalties going to balance the books. Russo, who came on board this summer, said one of his missions is to develop a fiscal structure that gives ART a substantial reserve fund. And Paulus has drawn fire at times for her tinkering with classic work for the sake of audience accessibility: She was taken aback when composer Stephen Sondheim laced into her publicly for tweaking the handiwork of George and Ira Gershwin and DuBose Heyward in her version of “Porgy.” (Among other things, she changed the famous ending, an alteration she ultimately abandoned.)

“No question it was a shock, because he was writing a letter without seeing the production,” she said of Sondheim. “I’m just sad he never saw it.”

Nevertheless, “Porgy” proved to be good fit for Paulus’s ART. It not only provided a bridge to schoolchildren in the Boston area — many of whose tickets were underwritten by the Gershwin Foundation — but also engaged a Harvard audience. In tandem with well-known Harvard professor Marjorie Garber, Paulus got the opera included in the curriculum. Porgy and Bess, Performance and Context was the course they taught together, just before the show played at the Loeb.

The Gershwin’s Porgy and Bess

directed by Diane Paulus. Wednesday through Dec. 29 at National Theatre, 1321 Pennsylvania Ave. NW. Visit www.thenationaldc.org or call 800-514-3849.b