What actor or actress really gave an exceptional performance, even though he or she was only playing a minor character. To be clear, I don't mean a supporting character, but a character that only appears in at most two or three scenes in the entire movie?

I'll get the obvious one out of the way first. Alec Baldwin in Glengarry Glen Ross.

O. P. Heggie as The Hermit in Bride of Frankenstein (1935)
Christopher Walken in True Romance
Christopher Walken in Pulp Fiction
Alec Guinness as King Faisal in Lawrence of Arabia

Kevin Spacey in Se7en

Gas station owner who isn't killed by Anton Chigur

I've always thought the motel clerk in Planes, Trains, and Automobiles gave an extraordinarily odd, dryly hilarious performance in a 60-second cameo.

Bronson Pinchot in Beverly Hills Cop

Alfred Molina in Raiders of the Lost Ark and in Boogie Nights

Robert Duvall in Apocalypse Now.

Julianne Moore in The Fugitive

Matthew McConaughey in Wolf of Wall Street.
Dave Sheridan in Ghost World
Bill Murray in Zombieland
Tim Robbins in High Fidelity
Steve Buscemi in The Wedding Singer
Harland Williams in Dumb & Dumber
Murray Rubin in Ghostbusters
Diedrich Bader in Napolean Dynamite
Diedrich Bader in Office Space.
Chris Farley in Dirty Work
Chris Farley in Billy Madison

Orson Welles - The Third Man
Gene Hackman - Young Frankenstein
Martin Scorsese - Taxi Driver
Ned Beatty - Network
William Hurt - A History of Violence

Mike Yanagita in Fargo

I don't think that the villain qualifies as a minor character. So I would exclude Harry Lime and John Doe.

Brad Pitt in 12 Monkeys

and another vote for Spacey in Se7en

I mean, she's in it briefly, but would you consider that an exceptional performance?
"Hey, Do you have a particular interest in our patient's X-Rays?"

Paul Kelly has a brief scene or two as Gloria Grahame's slightly looney husband in CROSSFIRE (1947). Minor character, brief screen time, but his scenes stand out for me more than any others in an otherwise star-packed film noir (Robert Mitchum, Robert Ryan, Robert Young, Sam Levene, etc.).

Kelly's the one on the far right here. He and Gloria are staring each other down.

Mark Strong - Body of Lies (2008) -- always thought he was fantastic in that small role - Oscar worthy in fact.

Michael Shannon - Revolutionary Road

Janet Leigh in Psycho-How long was she on screen before she met here end in the shower scene?

Steven Seagal in Executive Decision

Samuel Jackson in Deep Blue Sea

Exceptional performances? Absolutely. Minor characters? Hardly. Spacey plays the main villain, and Pitt is the leader of the titular group, so no I wouldn't say they're minor characters. Supporting, sure, but not minor.

Now if you talk about Brad Pitt in True Romance...

Ooh! Here's one!

Julia Butters in Once Upon a Time in Hollywood.

Ben Stein as the teacher in Ferris Bueller's Day Off
The disgruntled All-American Burger customer in Fast Times at Ridgemont High
Tommy Chong's father in the opening of Up in Smoke

Apparently she had a bigger part but much of it didn't make the final cut. In her two or three scenes that made the final cut she did really stand-out. Her subsequent success has certainly proven that.

Leland Orser never gets much love but his intense performances in both Se7en and Alien Resurrection are so damned memorable! He is the king of intensity!