There was never much doubt that the Alicia Keys musical, “Hell’s Kitchen,” was going to be on Broadway. Keys spent 12 years developing a loosely autobiographical jukebox of her songs, incorporating such hits as “Girl on Fire,” “Fallin’” and “No One.”

The problem is that while it played to sold-out crowds, the show that premiered at the Public Theater in November had herky-jerky pacing, a few too many groan-inducing scenes, and a second act that lost sight of whatever point the story was trying to make. (In his review for The New York Times, Jesse Green pointed out that, after the intermission, the show tumbled “directly into the potholes it spent its first half so smartly avoiding.”)

Yet here we are now, with “Hell’s Kitchen” at the Shubert Theater, a few blocks from where the show’s action is set. Having seen the first version last fall, I had jitters. But “Hell’s Kitchen” has earned its place on Broadway: The revised show is thrilling from beginning to end, and easily stands out as one of the rare must-sees in a crowded season.

All this happened without a major overhaul to Michael Greif’s production, which has a book by Kristoffer Diaz. The cast and creative teams are essentially the same, and there have been judicious tweaks and trims rather than radical changes. The main differences are further refined technical elements and, most important, a subtle but crucial change in focus.

That adjustment is evident from the start, with a new line that kicks off the story: “Because I’m your mother, that’s why.” We are thrown in the middle of what is clearly a recurring argument between the Keys stand-in, 17-year-old Ali (the sensational Maleah Joi Moon), and her mother, Jersey (Shoshana Bean, in top form). Jersey has been raising her daughter on her own, without much help from Ali’s father, Davis (Brandon Victor Dixon), and is very protective of her kid. Mother and daughter live just off Times Square, in the neighborhood of the show’s title, and Jersey is fearful that her daughter will fall prey to the streets’ many dangers — we are in the late 1990s, and Jersey is eager for Mayor Giuliani to “clean all of this right up.”