But in the same category, I have one that goes that one better. The title of Golden Smog's first full length album, Down By the Old Mainstream, comes from a song by a different band, Wilco--Someday Soon, off Being There. (The bands do have one member in common--Jeff Tweedy.)
Okay then, here a M3S for ya:
Stones - "Shattered"
Beatles - "Lovely Rita"
Doors - "Back Door Man"
Each spawned the title of an album by a different band:
Back Door Man: But the Little Girls Understand...--The Knack
Lovely Rita: Give Us a Wink--Sweet
Shattered: Love and Hope and Sex and Dreams--the BoDeans
I was pretty sure you were going for something like that, but yes, I had to look at the lyrics to the last two to get the specifics.