In a year when Lady Gaga stands to win at least one Oscar next month and has a decent chance at two, it may sound like a case of premature congratulation to suggest that she’s already enjoyed the most triumphant night she’ll have in 2019, if not in her career. But during Sunday’s opening performance of “Jazz & Piano” — her other residency show at the Park Theatre in Las Vegas — it was pretty clear that this trip through the statuesque heights of the Great American Songbook, not a gold statue, was her real dream come true. It was pretty dreamy for the rest of us lovers of Cole Porter, Billy Strayhorn and ridiculous headdresses, too.

“You know, it was just last night I was bent over in a thong singing some progressive pop,” the star quipped at the top of the show, making reference to “Enigma,” which opened three weeks ago, and which she had indeed been performing just 24 hours prior. It’s no insult to that other production — or to thongs, for that matter, or to flying harnesses and giant robots — to say that “Jazz & Piano” blows that one out of the water. You may enter the premises with the still reasonable suspicion that anyone who’s made it in contemporary pop will be the beneficiary of some automatic handicapping when they deign to go legit and go slumming through the standards of the ‘30s, ‘40s and ‘50s. But this show makes it clear that no one needs to put a pinkie on the scale while judging her prowess. The real test is imagining whether you’d still be this won over if you were seeing her do these songs as an unknown at the Rainbow Room… or as an actual Vegas star in an alternate 1960s universe where Shirley MacLaine is not the sole female Rat Packer. She passes, with flying and terrifically flamboyant colors.

The setlist for “Jazz and Piano” was more of a mystery in advance than the obvious greatest-hits lineup for “Enigma.” Would she even be doing any of her original material with an orchestra? She does, although it’s only four songs sprinkled into the show. Her due humility about that arrives in a filmed interview interlude where has her semi-apologizing for putting her compositions up there with Rodgers & Hart’s. But those four 21st century hits receive such fun new arrangements that you might wish she’d thrown in one or two more.

“Born This Way,” for one, actually should have been born this way, the way she sings it alone at the piano, as a sort of slow gospel number; it no longer sounds like a kicky “Vogue” knockoff but something more primal and spiritual, and it’s surprisingly moving in this more reverent frame. “Paparazzi” was preceded by a sober speech about the price of fame and how “it is legal to be followed” — even though, she self-consciously added, “I don’t mean to tell you a sob story in some velvet and diamonds” — and ended with the full orchestra kicking in with some apropos suspense-movie chase music. There was no such seriousness, of course, with “Poker Face,” which Gaga introduced with some setting-appropriate gaming talk before adding some critical metaphorical explanation. “Just like (with) many songwriters before me, people thought they knew what this song was about,” she said. “They were wrong… It’s when you’re with a man and you’re thinking about a woman — you gotta keep your poker face.” (“Sorry, MGM,” she deadpanned, shortly after singing the “bluffin’/muffin” rhyme, which is not an advertisement for the Park Hotel’s Starbucks offerings. “I already cashed the check.”)

As for the 16 vintage covers, many skewed toward expectations of what you’d see in this kind of show. She opened and closed by being Frank — the suddenly self-referencing “Luck Be a Lady” bookending on one side of the show and “New York, New York” closing it out. You wouldn’t deny her these opportunities to blow it out in the brassiest mode of New Jersey’s expat finest, but the more nuanced standards in-between offered better opportunities to suss out her real skills. “What a Diff’rence a Day Makes,” borrowed from her heroine Dinah Washington, benefitted from a shimmering string arrangement as well as Gaga’s own attention to the sense of newly born hope in the lyric. Her version of Cher’s hit “Bang Bang” was slow and dramatic enough that when someone laughed during a lull in the music, seemingly thinking the song was camp, Gaga interjected, in a seemingly spontaneous defense, “It’s not funny.” Her most exquisite performance came via “Someone to Watch Over Me” — no one would ever mistake Gaga for the Gershwins’ “lost little lamb,” but she’s effective at playing one on TV — and in nailing the challenging subtleties of “Lush Life,” using these ballads to bring out an exquisite vibrato she’s smart enough to use sparingly.

Gaga is clearly not into going into the obscure parts of the standards canon for obscurity’s sake, but it was nice to hear her pull out two numbers that would be rarely heard these days even on the cabaret circuit: “Orange Colored Sky,” not oft revived since its sentimental immortalization by Nat King Cole, which she described as a girlhood favorite, and “Little Coquette,” a Guy Lombardo-by-way-of-Fats Domino charmer that Gaga announced had already been set out as her funeral song. “You know, when they’re rolling me out — f— it,” she cheerfully declared. (Now if only she’d get her Little Monsters fan base to change their name en masse to the Little Coquettes.)

Kevin Mazur / Courtesy Park MGM Las Vegas

Early on in the show, Gaga announced that she had a surprise guest, quickly followed by the admission that it probably wouldn’t be a surprise to anybody… although it reportedly was, in fact, a fairly last-minute addition. That was the appearance of Tony Bennett, with whom she hooked up for a duets album and tour in the early part of this decade, still looking as pleased at 92 to be bearing Gaga’s lipstick imprint after her literal demonstration of “Cheek to Cheek,” and to be signing off on the cheeky idea that “The Lady Is a Tramp.” Her sweetness was fetching: “You don’t mind if I walk him off, do you?” she asked the crowd at the close of the two-song cameo. “Because it’s nice to just touch him.”

It was not her last gentlemanly moment, as there was a bit of proud androgyny to come. After the third and final costume change of the night, she appeared in a poufy black skirt over what looked like an acrylic tuxedo, then joked, “What’s funny about this outfit is, I got a skirt on and I’m a lady, but I take the skirt off, and now I’m just a gigolo.” What followed was a sing-along of the David Lee Roth… sorry, Louis Prima classic, in conjunction with her cabaret-haunting friend of two decades and other duet partner, trumpeter and musical director Brian Newman. Her other outfits were more leg- and/or décolletage-baring, sometimes looking like something out of the saluted era, and sometimes not, as when one pink number had shoulder pads nearly the width of the stage itself, or the opening “wig” that looked some a huge set of soft porcupine quills. Her ensembles might’ve seemed radical by Rat Pack-era standards, but not much more radical than standard-issue Patti LaBelle. She seemed well aware of the balance she was striking, in costume as well as song and general tone: entirely respectful of the classy showroom tradition, give or take just a couple of F-words and jaw-dropping 21st century accessories.

There were some groaners in the scripted material between songs, just as there are in the script for “Enigma.” Pretty much every rap between songs starts promisingly with a personal aside and ends in an awkward declaration of the following song’s title or key lyric. But it’s not as silly as “Enigma’s” attempt to establish a sci-fi narrative. She’s just following in just about every cabaret singer’s history of looking to establish some connective tissue between the tunes, however forced. She’s always on, even when she’s demanding a glass of whiskey, which she plops down on the piano with an audible thud that makes you think the top of the keyboard might’ve been mic-ed for just that purpose. But you could also tell, Sunday night, that there was some real emotion involved in this particular experience, for the girl who spent some of her underage years in drag bars just wanting to get into the meat of old Fred Astaire or Edith Piaf material before she ever dreamed of getting into a meat dress.

Piaf’s “La vie en rose” was just such a youthful moment she relived in Sunday’s opening, just as she relived it on screen in “A Star Is Born.” (It was the only song carried over into “Jazz and Piano” from her hit movie; sorry, no orchestral “Shallow” here.) If anyone imagined her performance of that in the film was a product of editing, either on screen or in the recording studio, her rendition of it at the Park put the lie to that idea: It was hard to imagine anyone short of Piaf herself singing it any better or more powerfully. It wasn’t just a bravura diva moment — though it certainly was that — but was something strangely autobiographical, too. In Lady Gaga’s world, there’s not a lot of distinction between the theatrical and the personal, or between her being royalty and being your New Yawk, New Yawk-accented BFF.

And it’s not just about her. The charts are a star of “Jazz & Piano,” too. The vast majority of the audience at the Park would have no way of remembering how much this show recalls peak Vegas, when you had to tip the maître d, not StubHub, to get this close to a world-class 30-piece band with a world-renowned belter in front. But surely everyone senses this is the best shot we’re going to get at that time travel… and that, if we did get into a wayback machine, we might find that some of the stars of yesteryear didn’t put quite as much of their all into their Glitter Gulch sets that Gaga is putting into hers. Of all the things you could do with a few hundred dollars of disposable income in Las Vegas right now, spending it on Gaga singing “Call Me Irresponsible” is actually the most responsible.

“Jazz & Piano” has eight repeat performances currently set at the Park, for February 3, June 2, 9 and 15, October 20 and 26, and November 3 and 9. As with the concurrently running “Enigma,” Gaga is expected to extend the engagement into next year.