“Black Nativity” is a musical updating of Harlem Renaissance poet Langston Hughes’ play, based very loosely on the way Jesus of Nazareth entered the world in a manger in Bethlehem. Once it finds its footing, this Harlem variation on the Nativity story manages to be sweet enough to touch people the way Christianity’s “Greatest Story Ever Told” always has.

Credit the cast, and a sympathetic handling of the material by writer/director Kasi Lemmons (“Eve’s Bayou”).

Jacob Latimore is Langston, a Baltimore teen who narrates his biography in rhymed couplets, but whose mom (Jennifer Hudson) faces foreclosure.

Mom packs him off to live with her estranged parents, a preacher (Forest Whitaker) and his wife (Angela Bassett). The Rev. Cornell Cobbs could have been just a judgmental stiff, mistrusting the 15-year-old who is no sooner off the bus than he’s robbed and accused of robbing someone else. In Whitaker’s masterful hands, the reverend betrays moments of guilt and a need to relate to this grandson he’s never known.

Bassett gives a busier performance, the very picture of a grandmother trying too hard to connect with the boy in the hope he’ll lead to a reunion with his mother.

Tyrese Gibson has his best role in more than a decade, playing a street thug who nicknames the kid “Lunch Money” while they’re in jail and whose life reconnects with Lang­ston’s throughout the story.

The great Vondie Curtis-Hall is a wise and streetwise pawnbroker who says he knew Langston’s dad. And Mary J. Blige plays an angelic parishioner at the Rev. Cobbs’ Holy Resurrection Baptist Church.

Langston has shown up on the eve of Christmas, and that church is famous for its “Black Nativity” pageant — a Kwanzaa-meets-New Testament spectacle that the kid, hung up on coming up with Mom’s mortgage money, isn’t interested in.

This being a musical, and one featuring the Oscar-winning Hudson, characters break into song, lamenting their lives, their lost childhoods or lost child. The music, by Laura Karpman and Raphael Saadiq, is forgettably generic modern soul with hints of hip-hop. But it is nicely integrated into the story and the production uses polished singers Hudson and Latimore to buttress the less-known-for-their-singing Bassett and Whitaker.

The sermonizing gets downright heavy-handed, but Lemmons wisely keeps the film brisk and brief. The high-minded “Black Nativity” is still a modestly entertaining and uplifting version of a “greatest story” that has proven as malleable as it is timeless.