Set a personal goal and achieve it (example, kill that guy more than I die, get one more tower, take the next dragon solo, etc).
Choose to reclaim from your teammates the permission you gave them to control your emotions.
Choose to see your teammates as amusing. It helps to imagine them as favorite (or least favorite) sitcom characters or celebrities. "Bieber, stop letting teemo kill you like tha--- never mind, as you were, carry on."
Imagine this match is the training montage right before your world championship game (next match). Playing "eye of the tiger loud enough to troll the neighbors helps, but is kind of mean.
Challenge the opponent in a solo lane to an emote contest: whichever of you can time your emotes to lane minion killing each other better gets a free kill on the other. Note: if your opponent is teemo, kill them while they're dancing.
Remember that it is a game and the purpose is to have fun. If the servers shut down forever right then you haven't lost anything. The experience is what it is and always will be about.
Play like it is the last game you'll ever play.