Count Basie is the one who was first. He won in the same year as Ella Fitzgerald. Many name both when the question is asked, but the answer is Count who won the award earlier in the show.
Best Female Vocal Performance
Ella Fitzgerald “But Not For Me.”
Best Jazz Performance, Individual
Ella Fitzgerald for Ella Fitzgerald Sings the Duke Ellington Songbook
Best Jazz Performance, Group
Count Basie for Basie
Best Performance by a Dance Band
Count Basie for Basie
Both artists later collaborated on an album “On The Sunny Side Of The Street” arranged by Quincy Jones.