When an 88-year-old singer releases a new album, critics usually scrutinize every phrase for signs of wear and tear. But Tony Bennett will get a free pass on his latest release, Cheek to Cheek.

Yes, his voice has aged gracefully, and even the little growl in his lower register, more noticeable in recent years, only serves to enhance the emotional impact of his songs. But that’s hardly the reason why his new album of duets will get front-page coverage in the entertainment media.

His female protégée is the real mystery here. Like Bennett, she is part of the long tradition of Italian-American pop vocalists. Her name is Stefani Joanne Angelina Germanotta. You know her better as Lady Gaga.

Believe it or not, Lady Gaga is now a jazz singer. I never expected that career move. If you had asked me, a year ago, to predict which pop superstar would release a jazz album, I might have guessed Adele or John Legend, or perhaps Beyoncé. Even Pharrell would have seemed a more likely choice. (Am I the only person who thinks that “Happy” has a jazzy, Les McCann-ish beat?)

I’ve viewed Gaga as more a performance artist than a musician. She is certainly a risk-taker and attention-getter, but often for matters of costume, props, and behavior. I never suspected a jazz singer might be lurking behind the meat suit, or inside the large plexiglass egg. Let’s be honest: There is zero jazz content in songs such as “Poker Face” or “Born This Way”—although no shortage of charisma and confidence.

Yet I’ve occasionally encountered another Lady Gaga, one that can be found in video clips of her at the piano or singing in less heavily produced and choreographed settings. And this young woman has a strong voice and good ear. She conveys a genuine interest in music as music, not just as part of a larger spectacle.

But can Lady Gaga really sing jazz? Jazz requires more than just hitting notes in tune without digital assistance, but also skills in conversational phrasing, bending and tweaking tones, floating over the beat, and handling a host of other demands in real time that can flummox even highly trained vocalists. You don’t just pick up these abilities overnight. I’ve worked, for example, with classical singers who possess amazing voices, but couldn’t deliver a convincing jazz ballad to save their lives.

Is Gaga up to this challenge? Can she interpret the works of George Gershwin, Duke Ellington, and Cole Porter with plausibility? Above all, can she trade phrases with Tony Bennett—and not get left in the dust?

The answer is, somewhat to my surprise: Yes, she can.

Now as a nitpicking jazz critic, I am not about to go gaga over Ms. Gaga, and will offer up quibbles and caveats about some aspects of her new persona. But I must give this Lady her due. As a jazz singer, she operates at a much higher level than any of us had a right to expect.

OK, she over-sings at times, and an occasional touch of shrillness enters her voice. But you could say the same about several celebrated jazz divas, for example Diane Schuur, who managed to win a couple of Grammy awards with a voice that could drown out a foghorn. And, in all fairness to Lady Gaga, any singer who matches up with Tony Bennett needs to get loud and assertive. Bennett believes that most songs deserve a big finish, and still—even in his late 80s!—can deliver the goods. You can’t be a shrinking violet and meet him on equal terms.

Gaga is especially convincing at slower tempos, and this is where weaknesses in phrasing are typically most exposed. Her voice projects an appealing innocence—I never thought I would use that word in regard to a Gaga album! Listen to her delivery on “But Beautiful” and “Ev’ry Time We Say Goodbye” for good examples. And at almost every juncture of this album, she communicates a disarming enthusiasm for the music. In truth, this occasionally moves her outside the spirit of the melancholy love lyrics she’s delivering. But most of her interpretative choices are sound, even on a song with challenging psychological depths such as “Lush Life.”

At this point, I must offer sympathy for all the talented jazz singers who have never had this kind of high-profile platform to show what they can do. When will Susana Raya get a record contract? Why isn’t Sara Gazarek better known? Or the boy wonder Jacob Collier? When will Cécile McLorin Salvant, Kurt Elling, and Gregory Porter rise from the ranks of jazz stars to enjoy genuine crossover fame? I have a little list of 20 or 30 vocalists who deserve a chance to move from the margins of the music world into the mainstream. I can imagine every one of them looking at this Lady Gaga album and asking: “She didn’t pay her jazz dues, so why does she get this chance?”

On the other hand, I have a hunch that Lady Gaga will pay some heavy dues for this career move. She has already faced complaints that her recent Artpop album was a failure, even though it sold more than 2 million copies. True, compared to the 15 million copies purchased of The Fame at the outset of her career, a measly 2 million-seller represents a serious setback. But how can she come close to even those reduced numbers with a jazz album? Many prominent jazz artists struggle to sell 10,000 units, let alone 10 million. I can’t help but predict that Lady Gaga will lose a fair portion of her audience by aligning herself with such complex songs.

I won’t go so far as to claim that Lady Gaga is committing career suicide by embracing jazz. But this is clearly a move she is making for personal, rather than economic, reasons. History tells us that commercial artists who abandon the style that brought them fame often find themselves abandoned in turn.

But who knows, maybe Lady Gaga’s little monsters (as she affectionately calls her fans) will open up their ears and embrace classic jazz. Now that would be a remarkable achievement, even a bigger deal than matching Tony Bennett note for note.