Unilt the Night is from Billy Joel's 52nd Street album. There are two saxophonists with credits but I believe it is played by Richard Cannata, who performed another of the great Billy Joel sax solos - Scenes from an Italian Restaurant.
As a contrast here is a rare live version from 1998. (The audio quality is poor but just - barely - acceptable. It's still noticeable how Billy Joel's voice has changed though.)