cooler heads prevail
Calm people, thoughts, or actions triumph in the end. Thankfully, cooler heads prevailed in our fight against the school board, and we were able to reach a compromise.
prevail against (someone or something)
To overcome and succeed against someone or something. I believe as strongly today as I did when I was younger that love will always prevail against hate in the long run. No one expected our team to prevail against the defending champions, but we found it in ourselves to win.
cooler heads prevail
Fig. the ideas or influence of less emotional people prevail. (Used of a tense situation.) One hopes that cooler heads will prevail and soon everything will calm down.