Alice Cooper played two songs live on the Barry Richards show in 1971....seen only in Washington DC area but available on DVD. Great rocking version of I'm Eighteen but the real treat is the second song Black Juju. 13 minutes of Alice Cooper at their prime. ALICE COOPER - I'm Eighteen & Black Juju - YouTube
This one I think doesn't fit into the "perhaps most of us have never seen" category, considering the profile of a Grammy performance, but Aretha Franklin pinch hitting for Pavarotti, having literally been asked to do it by producers mid-broadcast, and bringing the house down with an aria that was Pavarotti's go-to number. The ultimate power diva move.
Lesley Gore performing ¨You Don´t Own Me¨ in 1988. Her middle-aged voice fits this song better than the original.