Justina Machado, Rita Moreno in Netflix's "One Day at a Time"
CNN  — 

“One Day at a Time” is that rarest of reboots, one that takes the bones of the original Norman Lear comedy that premiered in 1975 and transforms it into something fresh and vital. Buoyed by a terrific cast – including an utterly ageless Rita Moreno – it’s the kind of show that could give both TV’s nostalgia wave and the ailing sitcom format good names.

Granted, Netflix has toyed with that traditional multi-camera format before, including its undistinguished “The Ranch.” But this new show not only incorporates the familiar rhythm and laughter cues of a studio audience but incorporates serialized elements as well, along with genuinely heartfelt and touching moments, which is where the series really shines.

This “Day” dawns not only in a different era, but with a new ethnic flavor, starring Justina Machado (perhaps best known for “Six Feet Under”) as the daughter of Cuban immigrants, and an Iraq veteran. Separated from her husband, Machado’s Penelope is raising two kids (with a gender modification from the original), with help from her mom (Moreno), who gets all the best lines.

Penelope currently works as a nurse, with the always-funny Stephen Tobolowsky as her doctor boss. When an elderly patient says something inappropriate to Penelope, he says the woman has Alzheimer’s, then deadpans, “I’m messing with you. She’s just racist.” Additional silliness comes from Todd Grinnell as Schneider, Penelope’s ever-present, womanizing landlord.

The premiere features the family planning a quinceanera, or 15th-birthday celebration, for Penelope’s daughter, Elena (Isabella Gomez), a brainy type who proclaims the tradition a “misogynous cultural ritual,” much to grandma’s horror.

What could be predictable in its efforts to be topical, though, yields an abundance of pleasant surprises. That includes stretching out the party planning over the entire 13-episode season, and plenty of heartfelt moments, such as Penelope’s tearful monologue about the strain of being a single mom, which is real and touching.

Those kinds of sequences keep surfacing, feeling organic rather than forced. Elena, for example, chafes at being considered a “diversity candidate,” while other twists punctuate a second half of a season (all the episodes were made available) that gets stronger toward the end.

Credit producers Gloria Calderon Kellett and Mike Royce, who oversaw the revival with input from the 94-year-old Lear, with managing to make the more sober aspects reside harmoniously with the comedy. Moreover, at a time when the major networks are pretty starved for hit comedies, to quote the song, this is it – the kind of polished product anyone should be proud to have.

It helps, that while the ’70s version was a popular, long-running show – Valerie Bertinelli grew up on TV – it’s not the sort of series where it feels like sacrilege making it over. Still, even if the resemblance is relatively modest, Netflix’s updated take does a whole lot better than just muddle through.

“One Day at a Time” premieres January 6 on Netflix.