Katy Perry to John Mayer -- You Make Me Feel Like a Natural Woman

John Mayer and Katy Perry partied like 18-year-olds ... clubbing till 4:30 AM Thursday, and that's after John raged onstage at a concert earlier in the day with the Grateful Dead.

Check out the clip below ... John and Katy were at The Nice Guy in WeHo, when the crowd became church mice as she sang "Natural Woman." You hear guitar, which we're guessing is all John.

They've been together for a long time now ... seems like a good fit.