Name that tune!

Last Friday I bought The Essential Bruce Springsteen, and when I heard the song Badlands, I immediately recognized the piano part as coming from an older song. Take a listen for yourself …

Badlands clip

Do you know what song it's from? Does it at least sound familiar? To be fair, I wasn't able to pinpoint the exact song until Wednesday afternoon while I was taking a walk outside. I'll post the answer in a day or two, or after someone guesses correctly.