I've found that saying "We're obviously both upset at he moment - can we talk about this later when we're both calmer" can also be quite powerful. It takes the wind out of the sails of someone who wants a fight, and it*genuinely* allows time for everyone to back off and calm down without losing face where you're dealing with someone who is normally reasonable but who has temporarily lost it!
I learnt this when I had a boss who was a bully. His technique was to continually goad people until they snapped and responded in kind, then *they* would be in the wrong for shouting at him... I am not confrontational and so, without any per-planning did suggest that we speak about the incident later when he was calmer. It stopped him dead. He was still a bully, but he didn't try that particular tactic on me again.