I might be the only one that enjoyed this brawl.
My strategy: Use a hero with a hero power that can hit the face Hunter/Mage/Druid/Rogue. General rules:
1. Play on curve.
2. If you have a minion you want to kill another with or hit face, do that before playing any new minions.
3. If you are ahead by some luck and can do a lot of damage, hit face.
4. If you are ahead, play fewer minions - such as one on curve - to prevent RNG issues. If you are ahead by a lot, don't even play a minion that turn. Hit face with minion and hero power.
5. If you are behind, say on turn 8, play as many low cast minions as you can and see what happens. See what random spell happens each time before adding more. I've seen both characters healed to max multiple times, as well as clearing the entire board too.
I've probably played this brawl 30-40 times. I've gotten both a turn 1 CoTW and had that go against me. Don't take it too seriously.