Beatrice Straight in Network won the Oscar for Best Supporting Actress for her five minutes onscreen. She played the devastated wife of William Holden, who reveals he has been having an affair and will soon leave Straight.
Trivia note: Network Director Sydney Lumet wanted to cut Straight's scene because they felt it wasn't working with the scene that followed it - the "romantic" getaway between Holden and Faye Dunaway. Film editor Alan Heim really liked the scene so much; he switched the two scenes so that Straight's scene came after the Holden/Dunaway scene. So Straight had Heim to thank for her Oscar!

Judi Dench won the Oscar for best supporting actress for an eight minute scene in Shakespeare in Love.

William Hurt in "A History of Violence" appeared in 1 scene, I think.

Ned Beatty/Network, John Lithgow/Terms of Endearment, Robert Duvall/Apocalypse Now, Brad Dourif/One Flew Over the Cuckoo's Nest and Mark Wahlberg/The Departed come to mind.

Christopher Walken in
Catch Me If You Can
had very little screentime. I don't think Dan Aykroyd had much screentime in
Driving Miss Daisy
, either, but I may be wrong on that.