I've often heard that cited as one of the least-deserved Oscars ever. But I've never seen the film and don't know who her competition was, so I've no idea.
My nominee for that distinction is also in this category, but 21 years later:
1990
Whoopi Goldberg -
Ghost as "Oda Mae Brown" (winner)
Annette Bening -
The Grifters as "Myra Langtry"
Lorraine Bracco -
Goodfellas as "Karen Hill"
Diane Ladd -
Wild at Heart as "Marietta Fortune"
Mary McDonnell -
Dances with Wolves as "Stands With A Fist"
If I'd been in charge either Bening or Bracco would have won, but winner would have certainly come in 5th. In fact I'd probably be able to find several more deserving performances to give her nomination to in the first place.