Leave it to a piano player who knows his New Orleans repretoire like few others (seriously - and I'm including a lot of locals), to come up with this gem, and an orginal rendition at that (though I never heard the Turner version).
As an aside, Booker (the Piano Prince of New Orleans) was an incredible player - boogie, barrelhouse, blues, classical, creole waltz - stuff you never heard of. He could glide effortlessly from one end of the keyboard to the other, and would all the time do things like throw a classical run into the middle of a blues piece. His style was continuos, spontaneous improvisation. He also had a terrible drug habit - died relatively young. That and his unique "Unclassified" style is why he's not better known.
One very sad night I'll never ever forget, Booker was playing the intermission at a club called Snug Harbor. A little while after he finished, I went to the restroom to find him on the floor sprinkled with his own vomit. I found some people who knew him better than I - they put him in a taxi - he seemed at least somewhat recovered by then. I guess he got home alright, and inside as well, but they found him dead the next day.
It was an immeasurable loss for us here, and for all the world who didn't get to know him better.