Prince Dearly Beloved ... Alicia Keys & Jennifer Hudson Pay Tribute

4/22/2016 7:31 AM PDT

Prince Tributes from Alicia Keys & Jennifer Hudson

Prince was all over NYC ... with Alicia KeysJennifer Hudson and the whole cast of "Hamilton" saluting the singer.

Alicia's one of the few artists Prince allowed to cover his music. On her debut album she recorded a new version of "How Come You Don't Call Me" -- and during a private show Thursday night she played the song and thanked Prince for teaching her "how to be bold and brazen."

He got more props on Broadway ... Hudson and the cast of "The Color Purple" closed with a "Purple Rain" sing-along -- and the "Hamilton" crew stepped outta the 18th century for "Let's Go Crazy."