Ask HN: Advice on arguing with a person who yells to prove their point

I had somewhat of an unpleasant experience tonite, I won't get into the details but I was having a conversation with some people at a dinner party and one of them was very argumentative. I'm not one to stand by and allow someone to get away with making contrary statements backed up by false facts and was easily drawn into an argument. I tried laying out the reasons for my opinion but was shouted down and spoken over top of every time I opened my mouth. It got to the point where I became so frustrated I began to raise my voice and what began as an intelligent conversation eventually devolved into a shouting match between myself and this other person. Needless to say this has upset me to the point it is now 3am and I am unable to sleep so I figured I would ask how you folks would deal with this situation as I feel if this had occurred with someone at a work function, it could have a lasting effect on my career. The only thought running through my head right now is a quote "I learned long ago to never wrestle with a pig as you both get dirty but the pig enjoys it!"