If anyone doesn’t know what makes a star a star, then they can find out by getting over to the Palace where Liza Minnelli is playing a limited engagement. Of course, her mother, Judy Garland, also played what was announced as a limited engagement at the Palace in 1951 and performed there for a record-breaking 19 weeks. Whether or not Minnelli attempts to break that record (doubtful) or not, she is giving her fans another chance to see her give her all and more — even when that all and more is tempered by a voice that is now a bit frayed at the edges.

Minnelli’s increasing tendency to make mush of the lyrics wasn’t helped by a large on-stage band that, under the direction of Michael Berkowitz, succeeded in overpowering her. Some of us were grateful when popular pianist and the show’s musical arranger Billy Stritch was her sole accompanist.

On opening night, Minnelli’s energy level was visibly taxed (let alone her now wobbly vibrato) to the point of exhaustion. There were too many moments during the show when Minnelli tried to make light of her being seriously out-of-breath. Feeling the incomparable and very personal empathy and adoration that surfaces from the moment the 62-year-old entertainer appears in a spot at the rear of the stage, a fan would periodically call out, “I love you, Liza” to which Minnelli would shout back, “I love you, too.”

There is an exhilarating give-and-take element to Minnelli’s act that makes an audience embrace her every gesture, movement, note, and word (distinguishable or not). Still sporting her signature gamine haircut, she looks terrific and trim. Except for her decision to wear an unflattering oversized shirt that stopped at the crotch during the portion of the show that paid tribute to her godmother and cabaret star/author/musical arranger Kay Thompson, Minnelli’s wardrobe otherwise consisted of three stunning tunic top suits: sparkly white, shimmering black, and for the finale, glistening red.

Full appreciation of Minnelli comes when you surrender yourself to a classic tradition of vaudeville-like show business that has all but disappeared. One gets a glimmer of this in “A Palace Medley,” in which this forever disarmingly charismatic singer invokes the era that made audiences thrill to Nora Bayes singing “Shine on Harvest Moon,” Sophie Tucker singing her signature song “Some of These Days,” and Fanny Brice’s poignant and legendary theme song “My Man.” It is to be expected that the songs written by John Kander and Fred Ebb are highlighted during the concert, notably the obligatory “Cabaret,” which closes Act 1 and “New York New York,” a song that Minnelli can count on to provoke a state of fandemonium.

My favorites among the 18 or so songs include Minnelli’s dramatically conceived “What Makes a Man a Man” by Charles Aznavour, two familiar golden oldie rousers (not that we needed any rousing) “Clap Yo Hands” and “Liza,” by the Gershwins, and the gently and sweetly sung encore, “Have Yourself a Merry Little Christmas” from her mother’s hit film “Meet Me in St. Louis.”

Minnelli holds the stage alone until Act II when she is joined by Cortes Alexander, Jim Caruso, Tiger Martina, and Johnny Rodgers, who lend their vocal and dancing finesse to the briskly staged Kay Thompson segment. There is one thing you can be certain of — that Minnelli is not about to let her fans down, but rather has them on their feet cheering after every song. **

Liza’s At the Palace, through Sunday, January 4, Palace Theater, Broadway at 47th Street. $55 to $125. 212-307-4100.

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