On Thursday night, the Opera Orchestra of New York, led by its founder, conductor Eve Queler, did its job. It presented an opera rarely staged; and it did so with a cast of interesting, worthy, individualistic voices — voices that may be overlooked by establishment opera houses.

The opera was “I Due Foscari” (“The Two Foscaris”), by Verdi — libretto by Piave, based on a play by Byron. Piave also supplied libretti to “Rigoletto,” “La Traviata,” and a few other shows. Verdi’s music is moody, tense, caring — in other words, Verdian. And Piave’s libretto is very strong. Relationships between husband and wife, and father and son, and father and daughter-in-law, are touching.

The “two Foscaris” of the title are Francesco Foscari, Doge of Venice, and his son, Jacopo. The son has been falsely accused of crimes, and has suffered terribly at the hands of the Venetian state. The Doge has endured all of this stoically — not abusing his position, as he would see it, to aid his son. Jacopo is assisted by his wife, Lucrezia, who is a marvelous, loyal, Fidelio-like figure. The drama ends very, very badly — justice is not served.

For an old-fashioned opera, Ms. Queler had an old-fashioned cast, engaged in real, full-blooded opera singing. No mousy manners were apparent. This may have been a concert in Carnegie Hall, but it was still a stirring night at the opera.

Singing the role of Jacopo Foscari was Aquiles Machado, a Venezuelan tenor. He emits an impressive stream of sound — which can become a river of sound. And Mr. Machado sang this role with due ardor. He was robustly lyrical in cavatina, and robustly nimble in cabaletta. Occasionally, his high notes were strained, and, occasionally, he could have applied more nuance. Also, his voice is not especially Italianate — it is more Latin. But, given his origins, why shouldn’t it be?

I might mention, too, that Mr. Machado could have made a greater effort to free himself from the score — from the music in his hands and on his stand. But this is not an important objection.

Singing the part of Lucrezia was the American soprano Julianna Di Giacomo, recently heard at the Metropolitan Opera in Bellini’s “Norma” — she had the small role of Clotilde, but she still made you sit up and take notice. And you really had to take notice on Thursday night, in “I Due Foscari.”

Ms. Di Giacomo’s voice is big, juicy, pulpy, vibrant, beautiful — an outstanding instrument. The singer combines power and lyricism, the way Deborah Voigt did, when young (and the way she still can, when she’s with it). As Lucrezia, Ms. Di Giacomo was often scalding; but even when she was scalding, she was elegant. I might say further that this voice is big, cutting, and beautiful — which is rare. You can pretty easily get two for three, but not three for three.

In her singing, Ms. Di Giacomo might have shown more discipline now and then; some passages should have been more incisive, or more definite. Early on, she sang a fine high C, but her later Cs were poor — south of the target, for one thing. But this was nothing but a triumphant outing for this young soprano, and the audience cheered its head off.

As it did for Paolo Gavanelli, the veteran Italian baritone who sang the Doge and father. This is one of Verdi’s patented baritone roles — and patented father roles. Mr. Gavanelli indeed sang paternally, and well. There was authority in his voice, and there was benevolence in his voice. Indeed, you heard a morality — which Verdi has something to do with too, of course.

In tenderness, outrage, defiance, resignation, or pathos, Mr. Gavanelli was totally operatic. You had the sense of witnessing a real pro.

The smaller roles were satisfactorily filled, and I might mention in particular two young tenors: Guillermo Lagundino (Maryland) and Luke Grooms (Tennessee). (How cool a name is Luke Grooms? How cool a name is Aquiles Machado?) Those two young tenors sang freshly and promisingly.

Above, I mentioned two purposes, or virtues, of the Opera Orchestra: It presents little-known operas and puts forward interesting, often unusual singers. Here’s another wrinkle: Those singers come in all shapes and sizes; there is no worry about whether a man or woman will look the part.

Ms. Queler knows and appreciates “I Due Foscari,” as she tends to know and appreciate all the operas she presents. The orchestra was sometimes sloppy — for example, in its pizzicatos. But then, those pizzicatos weren’t much worse than those of the Boston Symphony Orchestra, on this same stage, a week and a half before. Verdi gives the cellists a lot to do in “I Due Foscari,” and sometimes they responded adequately, and sometimes they fell short. The chorus — the New York Choral Ensemble — was stout and competent.

Here’s one bit of news, from Opera Orchestra land: On this night, they dispensed with the usual fat libretto, and had supertitles instead. This is largely an advantage, I believe (although some like a libretto as a keepsake — and a libretto enables you to know what’s coming next). In addition to the words, some images of Venice were projected onto the stage. A little cheesy, but okay.