One measure of the greatness of Beethoven is that even his detritus is superior to many of the major compositions of other renowned composers. Aboard Bargemusic on the East River on Thursday evening, cellist Peter Bruns and pianist Annegret Kuttner included some of this flotsam and jetsam in their presentation of the master’s complete works for their particular instrumental combination.

Mr. Bruns, former principal of both the Dresden Staatskapelle and the Bayreuth Festival, is an exceptional artist. Now living in Leipzig, he divides his time between solo performances and selected teaching opportunities. He has a deep, woody tone with a shiny, polished veneer, a highly developed dexterity, and an innate understanding of expressive phrasing. His cello is a marvel of the 18th-century craftsmanship of the Venetian Carlo Tononi, and it was once owned by another pretty good cellist named Pablo Casals.

In their zeal for encyclopedic completeness, the pair offered a set of variations on “Bei Maennern, welche Liebe fuehlen” — trust me, you know this tune — from Mozart’s “The Magic Flute.” The piece, without opus number, begins in medias res, the melody already being tinkered with in the first few measures. It would be very easy to dismiss this tomfoolery as Beethovenian doodling unless one was familiar with his extraordinary sketchbooks and their tantalizing bits of profundity. In this solid and delicate performance, even fluff seemed significant.

Much meatier was the Sonata in F major, Op. 5, No. 1. Before Beethoven, sonatas for instruments with piano tended to feature the keyboard, as the Mozart oeuvre would indicate. Afterwards too, when Brahms entered the fray, the piano tended to dominate. But Beethoven rather self-effacingly (and uncharacteristically) tempers the natural advantages of his own instrument in favor of the joys of the violin, cello, and even horn. On this evening, Mr. Bruns’s ardent lyricism advocated strongly for the piece, while Ms. Kuttner’s tasteful accompaniment allowed him to soar. Honestly, to hear Mr. Bruns and his gorgeous vibrato is to have experienced something quite special.

After intermission, things heated up immeasurably. Offering more substantial variations, the duo played the 12 on a theme from Handel’s “Judas Maccabaeus,” WoO 45. These are by turns lively and sweet, forceful and delicate, animated and contemplative. It was worth the price of admission just to hear Mr. Bruns lovingly vibrate his A string and develop the gorgeous melody of the penultimate variant, as if Beethoven were simply pointing out how much more competent he was than Handel to enchant.

There is no better way to state this than straightforwardly: The rendition of the Third Cello Sonata in A major, Op.69 was a magnificent performance. I have heard Yo-Yo Ma and Emanuel Ax present it — and they made a wonderful recording back in the 1970s — but they were pale shadows compared to these players. This is one of the greatest pieces in all of Beethoven, written at the same time as the “Ghost” trio and the Fifth and Sixth symphonies. Just moments into the high main theme of the Allegro ma non tanto, featuring once again that intensely vibrating A string, I knew this was going to be a wild ride.

Beyond considerations of pure beauty of sound, the pair did not shy away from fast, challenging tempi, nailing the complex syncopations of the Scherzo with pinpoint accuracy (brava, Ms. Kuttner!). Mr. Bruns was in his glory in the introduction to the final Allegro vivace, a Beethovenian device wherein he squeezes in a slow movement — marked Adagio cantabile — as an apparent throwaway to warm upthe cello for the ecstatic run to the finish line. And that sprint was exhilarating, leaving the crowd wanting more. And there was more, a lot more — all you had to do was come back to the barge on Saturday or Sunday.