Sometimes, events wholly out of the theater’s control muscle their way onto the stage and quite unexpectedly enrich our perspective. So it is with this handsome revival, infinitely superior to the previous Broadway incarnation, a woefully bedraggled 1997 staging with Nell Carter as orphanage monster Miss Hannigan that ran for only 239 performances. One suspects that this kid- and adult-pleasing version, enhanced by Anthony Warlow’s gruff and robustly sung Daddy Warbucks, will be ensconced at the Palace for far longer.

The gifted comic actress Katie Finneran, a Tony winner for her supporting performance in a 2010 revival of “Promises, Promises,” here slips into the frilly wardrobe of the noted child-despiser Miss Hannigan, a role originated legendarily on Broadway by Dorothy Loudon and portrayed in the lamer 1982 film version by Carol Burnett. With her sexy, neurotic energy, Finneran should be a great fit for a self-dramatizing villainess you never totally hate but have to love to watch go to pieces. Accelerating quickly into shrillness — even Miss Hannigan’s signature song, “Little Girls,” is pitched too high for her — Finneran doesn’t let the audience fully embrace her joyous malevolence. We never feel enlisted in her quest to rise from the ranks of the losers.

Thanks, though, to li’l Lilla and a superbly assembled cast of supporting orphans — Emily Rosenfeld, Georgi James, Taylor Richardson, Madi Rae DiPietro, Junah Jang and Tyrah Skye Odoms — the sentimental center of “Annie” holds, just fine. The musical’s songwriters, Charles Strouse and Martin Charnin, and book writer, Thomas Meehan, front-load their show with numbers sure to beat back even the sternest resistance: Annie’s lilting ballad “Maybe”; the gleefully syncopated orphan anthem “It’s the Hard-Knock Life”; and, of course, the song that launched a thousand stage mothers, “Tomorrow.”

Coaxed by Lapine, who collaborated with Stephen Sondheim on “Into the Woods” and “Sunday in the Park With George,” among others, Crawford exudes the beguiling clarity of a kid unbowed by the hard-knock life. Her Annie is as egalitarian as we’d like to believe our country, at its best, might be. So lumps tend to rise in one’s throat as she mingles with the low as well as the mighty, whether in the tent camps of those made homeless by the Depression or in the Oval Office, where her optimism inspires FDR (Merwin Foard) to dream up the New Deal.

Matching Crawford vowel for lazy New York vowel, the Australian Warlow proves to be an ideal Warbucks, the warmth of the performance rising scene by scene. David Korins’s sets are both economical and inventive, especially the storybook rendering of the Warbucks manse. Although Andy Blankenbuehler’s dances are stingy with the tapping, Todd Ellison’s crisp music direction confers a robustness on Michael Starobin’s orchestrations.