OMG! "Obsession" -- after hearing this for the first time in ages at the BBQ Saturday. Is Dave psychic? (Or did he hear it on 95.7 MAX?)
this is Animotion, but didn't someone else do this too?
To answer my own question...
It was written by Holly Knight, one of the most successful female songwriters of the '80s (take THAT, Diane Warren). She wrote "Better Be Good to Me" and "The Best" for Tina, "Love is a Battlefield" for Pat B, and "RagDoll" for Aerosmith -- the list goes on. Her band, Spider, may have done it first, or maybe she did it solo (she wrote "Obsession" with Michael DesBarres). I do remember hearing a different version some time before Animotion came along.