The Cowboys won the fight on the field and one of the bigger ones off of it as well on Thursday night ... as a Dallas supporter absolutely pummeled a Giants fan in a tiff at MetLife Stadium during the big game in New Jersey.
The chaos erupted early in the evening ... when a man in a Troy Aikman jersey got so upset with a Lawrence Taylor supporter -- he began beating the hell out of the guy.
Check out footage filmed by a bystander .