Well, they only had to remake a jillion TV shows from yesteryear to finally get one exactly, perfectly right. Not only is Netflix’s reimagined “One Day at a Time” a joy to watch, it’s also the first time in many years that a multicamera sitcom (the kind filmed on a set with studio-audience laughter) has seemed so instinctively comfortable in its own skin. It doesn’t try to subvert or improve on the sitcom format; it simply exhibits faith that the sitcom genre can still work in a refreshing and relevant way.

At least some of this success is directly attributable to Norman Lear, the 94-year-old sitcom genius who counts the original “One Day at a Time” (which ran on CBS from 1975 to 1984) among his many successes, and lends his advice and approval to this new version as an executive producer. What Lear provides in spirit and inspiration is enhanced by executive producers Gloria Calderon Kellett, Mike Royce and Michael Garcia, whose combined credits include such recent hits as “How I Met Your Mother” and “Everybody Loves Raymond.”

This “One Day at a Time,” which streams Friday with a 13-episode season, is much more than another nostalgia trip, yet it’s worth noting how much of the original story has traveled the decades intact. The premise is still about a recently separated working mom with two kids — only this time, the lead character is a 38-year-old Cuban American nurse and Afghanistan war vet named Penelope Alvarez (Justina Machado). Penelope left her husband, who is also a veteran, because of his issues with drug and alcohol addiction and his unwillingness to seek counseling for post-traumatic stress disorder.

Penelope works in the offices of a daffy general practitioner (Stephen Tobolowsky); her 14-year-old daughter, Elena (Isabella Gomez), and 12-year-old son, Alex (Marcel Ruiz), attend a nearby Catholic school. For help with all this, Penelope’s mother, Lydia (Rita Moreno), lives with them and meddles in every aspect of their lives.

Instead of the older show’s Indianapolis setting, this one is set in the Echo Park section of Los Angeles. In a nice touch, the floor plan of the Alvarez apartment is precisely the same as the one inhabited by Ann Romano and her daughters all those years ago — with Lydia living in the alcove off the living room, separated by a curtain that Moreno dramatically parts for her grand entrances.

And yes, this “One Day at a Time” comes with its own take on Schneider, the boundary-challenged but beloved superintendent first played by the late Pat Harrington Jr. This 2017 Schneider, played by Todd Grinnell, is ingeniously (and humorously) reconceived as a Gen-X trust-fund hipster — less tool belt, more selvage denim and Warby Parker specs — who owns and maintains the building and has become a token fifth player in the Alvarezes’ daily dramas. In Schneiderly tradition, he’s in their apartment more than his own.

As it was long ago, “One Day at a Time” leans heavily on Lear’s knack for fearlessly blending controversial topicality with comedy — with a sometimes challenging additional layer of identity politics. The Romanos and Alvarezes share a propensity for letting it all hang out — raised voices, slamming doors, a range of hurt feelings. They argue about the existence of God and going to Mass. They debate immigration. Schneider unwittingly strolls in wearing a Che Guevara T-shirt and gets a long harangue about the devastation of the Cuban revolution.

With a jaunty remake of the theme song from Gloria Estefan, the show opens with Lydia and Penelope making plans for Elena’s quinceañera, the traditional coming-out soiree for 15-year-old Latinas. As a budding feminist who is also questioning her sexuality, Elena isn’t having it: “I don’t want to be paraded around in front of the men of the village like a piece of property to be traded for two cows and a goat,” she says.

“Someone thinks she’s special,” Lydia remarks. Moreno, the living legend who at 85 plays a woman a decade younger than herself, excels at the role, luxuriating in an abuela’s opportunities to convey a rich sense of culture and faith to those around her, while getting most of the big laughs. Lydia’s endearing stubbornness lends “One Day at a Time” its most funny and most meaningful moments.

[Rita Moreno on strength, stamina and the power of a killer body]

But Machado, playing the role that the late Bonnie Franklin made so memorable, is a worthy equal to Moreno, helping her children reconcile their grandmother’s romanticized past with 21st-century realities. And, like Ann Romano, Penelope must also deal with affronts to modern womanhood, such as her discovery that the office mansplainer (Eric Nenninger) earns significantly more than she does even though they have the same job. Other relevant topics include Penelope’s ongoing struggle to get VA assistance for a lingering war wound, which leads her to a support group for women veterans led by original “One Day at a Time” cast member Mackenzie Phillips, in a cameo role.

Grinnell’s Schneider takes a little longer to jell, but he’s worth it. The writers have retained the original Schneider’s inflated sense of self (and libido), but they’ve also discovered a ready and willing father figure for the children.

Thus far, the sitcom format, which is so integral in the history of commercial TV, has struggled to find a home on Netflix, where original episodes can run eight or nine minutes longer than the 22-minute broadcast format and lead to a sense of bloat. “One Day at a Time” benefits by adding a few story lines that recur throughout the season and encourage binge-watching, including the inevitable return of Penelope’s estranged husband (James Martinez).

I knew that this “One Day at a Time” was working by the second episode, when I felt the same sense of investment that I used to feel as a child who faithfully watched the original and absorbed its strident stances on equality and personal independence. For years, critics lamented the disappearance of the way Lear and his collaborators gave their sitcoms an edgy point of view. They certainly had that, but what they were also good at was inviting a viewer in, no matter who you were, and making you feel at home — even if that home belonged to Archie Bunker or George Jefferson. This show feels like home.

One Day at a Time (13 episodes) begins streaming Friday on Netflix.