Friday night was a fantastic night at the Metropolitan Opera. Why? On the stage was Puccini’s superb triple bill, “Il Trittico.” It appeared in a splendid new production by Jack O’Brien. In the cast, or casts, were some of our best singers, and most of them were in top form. James Levine was in the pit, and he, too, was in top form — which is some form. And the Met orchestra played sensationally well.

Yes, it was a fantastic night, with everything and everybody cooperating.

“Il Trittico” means “The Triptych,” and its three one-act operas are “Il Tabarro” (“The Cloak”), “Suor Angelica” (“Sister Angelica”), and “Gianni Schicchi” (the main character’s name). The first opera is about an adulterous affair turned fatal. The second is about the travails of a misused nun. And the third — one of the most beloved comedies in opera — is about a scheming aristocratic family and the country sharpie who out-schemes them. This is a masterly trio of shows.

Jack O’Brien is having a big moment at Lincoln Center, for he is doing not only “Il Trittico,” but also Tom Stoppard’s “Coast of Utopia” (another triptych, as it happens). The Puccini evening requires three productions, really, and each of Mr. O’Brien’s fits the opera to which it belongs. These productions look, smell, and feel like their operas. Everything is natural and matching, and nothing is foreign or contrived. Douglas W. Schmidt’s sets, Jess Goldstein’s costumes, Jules Fisher and Peggy Eisenhauer’s lighting — not a thing can be argued with.

Seldom is a project so big and complicated categorically right.

James Levine began the Met’s current season with Puccini’s “Madama Butterfly,” and he had a rotten night back then. (Mr. Levine, I mean, not Puccini — well, Puccini did, too.) But Mr. Levine was an ideal Puccini conductor on Friday night. Take “Il Tabarro”: The score was beautiful — extremely beautiful — but it was also compact and solid. A measure of restraint made the emotion all the greater. Mr. Levine summoned up a tension that went through your bones. Even in calm sections, this music had murder written all over it.

And the orchestra played so well — so accurately, so cohesively, so responsively — it was almost out of its mind.

In the role of Giorgetta was Maria Guleghina, known as a rugged, powerful soprano, a battleship of a soprano, which she is. But she is not unnuanced or unmusical, and she is a compelling actress — a complete operatic performer. So she proved in “Il Tabarro.” Portraying Michele was Frederick Burchinal, substituting for an indisposed Juan Pons. Mr. Burchinal sounded tight and squeezed, and he at times could not be heard. But he was moving, getting the job done.

The tenor Salvatore Licitra was Luigi, and he was robust and heroic — meeting the expectations that the world has set for him. The mezzo-soprano Stephanie Blythe was Frugola, huge-voiced, technically sure, and delightful. She brought zest and relief to the goings-on.

David Cangelosi gave us a vibrant, interesting tenor as Tinca, and the bass Paul Plishka was a fine Talpa — still putting it out, in his 40th year with the Met.

In the title role of “Suor Angelica” was Barbara Frittoli, who was regal, sensitive, and commanding — a genuine Italian soprano. She sang the big aria, “Senza mamma,” with musical and dramatic understanding. The aria was slowish, and a high A was subpar — bad, actually. But Ms. Frittoli made her points, and she sang much better high notes later (including Cs).

Ms. Blythe was back, this time as the Princess, who is the Cruella de Vil of “Suor Angelica.” Our Stephanie was indeed a devil in a black feathered cap. She suffered some jarring lapses in intonation, but otherwise delivered. The opposite of this devilish character was Heidi Grant Murphy’s Sister Genovieffa. Pardon the cliché, but HGM sang like an angel, as she so often does. Her sheer radiance and goodness fill up a house.

And the mezzo Wendy White was the Monitor, sounding sturdy, abbess-like. I half-expected her to sing “Climb Ev’ry Mountain.”

“Gianni Schicchi” is a hilarious, super-deft opera, and Mr. O’Brien stages it in a hilarious, super-deft way. He milks the material, yet he avoids overmilking — nothing is too hammy or campy.

And Mr. Levine and his orchestra were simply dazzling in the score. They were colorful, sly, crackling, amusing — a little jazzy. And stunningly virtuosic. They turned “Gianni Schicchi” into an orchestral tour de force.

The title role was taken by Alessandro Corbelli, a baritone of noteworthy theatrical and other gifts. He was a treat to see, and hear. A tenor named Massimo Giordano — not to be confused with another Italian tenor, Marcello Giordani — was Rinuccio, and he was earnest and ringing. The soprano Olga Mykytenko was Lauretta, which meant that she got to sing one of the world’s favorite arias: “O mio babbino caro.” She did this in a lovely, unaffected way — first-rate. And Ms. Blythe did one more turn, filling the role of Zita. Among Ms. Blythe’s abilities is comic timing. She was a lovable, formidable hoot.

The Met audience more than got its money’s worth in this triple bill. Even those in the priciest seats more than got their money’s worth. And fantastically good as James Levine was, who was the number-one star of this evening? Giacomo Puccini. “Il Trittico” is the fruit of a phenomenal mind and pen. Next time someone tries to knock Puccini to you, don’t even bother to scold or laugh. Just roll your eyes and walk away.

Until May 12 (Lincoln Center, 212-721-6500).