Not sure if you'd consider some of this "classic rock" but it's all old:
- REM - Begin the Begin from Lifes Rich Pageant (actually that entire album is great)
- 10,000 Maniacs - Verdi Cries from In My Tribe (another great record and what a voice)
- Blue Oyster Cult - Black Blade from Cultisaurus Erectus
- Bob Segar - You'll Accomp'ny Me or We've Got Tonight (Bob Segar had so many hits but you really don't hear much about him now)
- Chickenfoot - not classic rock but if you like classic rock, both records are really good
- Cream - Swlabr from Disraeli Gears
- Iron Maiden - Murders in the Rue Morgue from Killers (both Killers and Number of the Beast are great back to back albums with different singers)
- Jeff Beck - Thelonious from Blow by Blow (another great album back to back)
- Jeff Beck - Star Cycle from There and Back
- Ozzy Osbourne - S.A.T.O. from Diary of a Madman (that album and Blizzard of Ozz are both great records)
- Porcupine Tree - Blackest Eyes from In Absentia
- Queen - Long Away from A Day at the Races
- The Police - So Lonely from Outlandos d"Amour
- Thin Lizzy - Cowboy Song (but the best version is when they combine it with The Boys are Back in Town from Live and Dangerous. Boys are Back in Town is not really a "hidden" gem. Just a gem.)
- Van Halen - Ice Cream Man from Van Halen
- Anderson, Bruford, Wakemen, and Howe - Brother of Mine