Liz McCartney and Kaitlyn Davidson perform in “Rodgers + Hammerstein’s Cinderella,” which is playing at the National Theatre through Nov. 29. (Carol Rosegg)

The enduring charm of Rodgers and Hammerstein’s “Cinderella” has become more of a charm offensive now that it’s a full-blown Broadway show. Not to worry, though: Although the 1957 TV special written for Julie Andrews has bulked up to resemble a 21st-century Disney stage spectacle, its basic sweetness still shines through.

Winsome is the way to be in this broad yet elegant musical comedy, rebranded as “Rodgers + Hammerstein’s Cinderella” when it debuted on Broadway in 2013. (It closed in New York earlier this year.) The touring version at the National Theatre through Sunday is a big storybook show, with grand dances and gee-whiz magic in the brilliant costumes by designer William Ivey Long.

This “Cinderella” is substantially different from previous versions of the Rodgers and Hammerstein property, but then there have been so many takes in the past half-century that you can’t be a purist about the original. (Varying TV versions starred Lesley Ann Warren in the 1960s and Brandy in the 1990s; the Olney Theatre Center’s most recent staging was in 2012.) The big change here is the updated book by Douglas Carter Beane, whose comic credits include the musical “Xanadu” and the play “The Little Dog Laughed.” Beane’s “Cinderella” plot involves more class warfare than usual, because a populist firebrand named Jean-Michel (an earnest David Andino) is now on the scene. The peppy dialogue has the light snark of animated movies.

“Okay, creepy,” Prince Topher says nervously during a royal ball when a predatory stepsister stalks him. The lingo is frisky; the kids giggle along.

Director Mark Brokaw’s staging occasionally amps the action high, starting with a battle scene in the forest as Topher subdues a giant aphid (or something). The squabbles and chases can be a bit frenetic, yet the show never loses touch with its cool, sophisticated musical core. The light Richard Rodgers-Oscar Hammerstein II songs are still insinuating: “In My Own Little Corner,” “Impossible” and “Ten Minutes Ago” are lovely, lilting numbers you want to keep in your head as long as you can. They’re wonderfully performed, especially by the completely fetching leads. (The orchestra of about a dozen is mostly up to the task.)

“Rodgers + Hammerstein’s Cinderella” is playing at the National Theatre through Nov. 29. (Carol Rosegg)

Kaitlyn Davidson is a gentle, determined, wholly adorable Ella; she sings confidently and dances with balletic aplomb, effortlessly lifting a toe over her head and sinking into one deep ballroom dip after another. Davidson connects smartly with Andy Huntington Jones’s aw-shucks Prince Topher. The romance clicks.

So does the enchantment when Cinderella’s fairy godmother (a warm, full-voiced Liz McCartney) shows up to make a miracle or two. Long’s costumes really do pull magic out of a hat — or out of a frock, to be more accurate — and Cinderella’s transformations never fail to delight.

Even with Beane updating Hammerstein’s book, all the classic elements are in place: a bright palace, a dingy lair dominated by an evil stepmother (Blair Ross, doing the gargoyle thing very well) and a ballroom filled with swirling dancers in bright outfits. Aside from some wised-up moves during casual scenes at the ball, Josh Rhodes’s stately choreography is traditional yet effective.

You can’t say that “Rodgers + Hammerstein’s Cinderella” has finally been perfected; it has been altered so often that by now it’s sort of a Frankenstein creation. There’s a totally modern power-ballad quality to a number late in the show, and new material includes “Now Is the Time,” cut from “South Pacific” and sung by Jean-Michel. Our dear “Cinderella” changes and spins and changes again, and this version will do, handsomely. Its spirit is right.

“Rodgers and Hammerstein’s Cinderella,” music by Richard Rodgers, lyrics by Oscar Hammerstein II, new book by Douglas Carter Beane, original book by Oscar Hammerstein II. Directed by Mark Brokaw. Music adaptation, supervision and arrangements, David Chase; orchestrations, Danny Troob; scenic design, Anna Louizos; lights, Kenneth Posner; sound design, Nevin Steinberg. About 2 1/2 hours. Through Nov. 29 at the National Theatre, 1321 Pennsylvania Ave. NW. Tickets $48-$108, subject to change. Call 800-514-3849 or visit www.thenationaldc.com.