The late singer won in the best rock performance category and his children Toni and Christopher accepted the award.
"I never thought we'd be standing here without my dad", said Cornell's son, Christopher. I'm sure he would be proud and honored.More news: Morgan Stanley to buy Canadian employee stock manager for $900 mln
"CORNELL DESERVES IT! The guy truly had an awesome raw and powerful voice", another added.
'It was very difficult because, obviously, we miss him so much and we saw him work on this so hard - he was always working on it music [because] it was his passion, ' the 14-year-old shared.
Yesterday's win for best rock single marked the grunge icon's third Grammy - his first as a solo artist. "While he touched the hearts of millions, the most important thing he is known for, to us, is for being the greatest father". Some 17,505 fans came from far and wide to celebrate his legacy.
Cornell's widow Vicky also attended the ceremony.More news: Chelsea 'exploring Tiemoue Bakayoko, Franck Kessie swap deal'
When the singer's nomination was announced back in September, his wife tweeted from his account, "Chris would be so proud".
As of this writing, Soundgarden have not confirmed a reunion, but the three surviving members - Kim Thayil, Matt Cameron and Ben Shepherd - have expressed interest in getting back into the music scene - whether that would be as Soundgarden is unclear.
Toni and Christopher Cornell said the tribute was "amazing".More news: Tottenham boss not surprised by Jadon Sancho's heroics at Borussia Dortmund