I can't decide on which actual gunfight, so I'm going to go with the scene in Tombstone where Kurt Russell as Wyatt Earp drives Billy Bob Thornton as Johnny Tyler out of The Oriental with no shots fired.
Johnny Tyler: You run your mouth kind of reckless for a man that don't go heeled.
Wyatt Earp: No need to go heeled to get the drop on a dub like you.
Johnny Tyler: Is that a fact?
Wyatt Earp: That's a fact.
Wyatt then slaps Johnny silly, and Johnny can't find the stones to draw.
Hokey religions and ancient weapons are no match for a good blaster at your side.