Last year, I suggested re-evaluating the list of the “big five” American orchestras. With the Minnesota Orchestra’s terrific performance at Avery Fisher Hall over the weekend, it may be time to revisit the list.

The Minnesota Orchestra has a long and special relationship with the Symphony No. 1 of Gustav Mahler. Although the composer was associated with both the Vienna and New York Philharmonics, it was the Minnesotans — in the 1940s, still called the Minneapolis Symphony Orchestra — who recorded the first pressing of this glorious work under their forward-thinking conductor Dmitri Mitropoulos. Mitro went on to New York, where he and his successor Leonard Bernstein turned Mahler into a household name, at least among record collectors.

Osmo Vänska is at the head of this fine assemblage now, and he led one of the best local live versions of this symphony in many years. During the first movement, there were a few gaffes to be sure, but overall the orchestra established itself as the possessor of a polished sound, the violin section especially sweet.

Mahler inherited from his mentor Anton Bruckner an insecurity about his own compositional talents, and so excised a movement of this symphony early in its creative life. Known as the “Blumine” movement, this nostalgic tone poetry landed on the cutting-room floor. Mahler soon had regrets over its exclusion, though, and a part of the famous post horn solo in his Third Symphony recalls the original movement’s lovely main theme. Unfortunately, Murphy’s Law held sway this day, as the trumpeter botched his important opening solo, although he recovered nicely for its reprise. Mr. Vänska’s scholarship and assiduity could not save the moment, but he deserves high praise for resurrecting such a beautiful orchestral interlude.

We vegetarians adore the third movement — well, in this performance the fourth movement — of this piece, as it depicts the creatures of the forest parading the trussed body of a hunter on a pole heading for the barbecue. Mr. Vänska asked for something puzzling at its beginning. The main theme — what we know as “Frère Jacques” and Mahler knew as “Bruder Martin” — is normally intoned by a solo bass fiddle. In this rendition, the entire section played it. After this initial shock, Mr. Vänska led a flawless performance, one that will remain in the memory for a long while. He is especially adept at emphasizing the difference between legato and staccato, holding his hand steady through a long note and waiting until the final millisecond to twist his wrist indicating a sharp, accented turn. His players followed enthusiastically.

The finale was pure joy, as Mr. Vänska was not afraid to hold notes beyond their rhythmical limits for dramatic effect. Even the trumpets were triumphant at the work’s conclusion, and when the eight horns, who were superb all day, stood for their final measures, I found myself shivering with delight. Isn’t this the way Mahler’s First is always supposed to sound?

Prior to this wonderful experience, the orchestra accompanied Lars Vogt in a strident and powerful Piano Concerto of Robert Schumann. Mr. Vogt was letter-perfect this day, choosing to emphasize the forceful, dynamic aspect of this music, rather than its equally compelling gentle, romantic side. Both interpretations are justified, each but one of many facets in the diamond that was Schumann’s amanuensis and the concerto’s dedicatee, Clara. The balance between soloist and orchestra was just so.

Mr. Vänska is Finnish, and all schoolchildren in Finland swear an oath to promote the music of their homeland, so we were treated to a tiny curtain raiser by Sibelius titled “The Dryad.” It is a shimmering piece of impressionism played with tender, loving care, and we were all the richer for having heard it.