Also, biting the upper arm area and hands are good too. Ever been lightly bitten by a dog in play and your whole hand goes numb? Think of that but 1000 times worse as you bear down, trying to crunch bone.
The only problem with trying to hurt the guy is that pain doesn't usually lead to a guy calling "uncle" to stop the fight.
You said yourself how your last fight ended...someone lands a (usually lucky) haymaker and the other guy gets knocked out. That's how pretty much every fight I've ever seen has ended.
You can try hurting the other guy all day, but the fight is going to end like every other drunken windmill-punching fight....someone lands a wild punch and other guy goes to sleep, or some asshole friend of one of the fighters sucker punches the other guy (and then does that "I'm a tough guy" dance with both arms locked straight down at his sides while hopping around and yelling "what's up now bitch?!?" ...everyone knows the sucker-punch tough guy dance).