The Grammys are the United States recording industry's most popular music awards.
Nelsons and the Boston Symphony Orchestra won the 'Best Orchestral Performance' award for their version of Shostakovich's Symphonies number 5, 8 and 9.
Responding to the news on Twitter, Nelsons said he was honored to receive the award for the second year in a row, having scored success with more Shostakovich last year in part one of the same series of recordings, under the title "Shostakovich Under Stalin's Shadow".
"It's an absolutely extraordinary but natural event. Because, when I got my hands on this album with three symphonies by Shostakovich, I realized that, if the previous album won a Grammy, this one should be thrice as awarded, as the result is excellent, wonderful," said Andris Dzenītis, program curator at Latvian Radio 3.
"Especially the interpretation, which will remain in the world's record archives for a long time as an original standard," said Dzenītis.
You can read more reaction to the award at the Boston Globe.
(The story was updated with Dzenītis' reaction and the image gallery.)