One of my favorite fights I would show a MMA newbie is Martin Kampmann vs Drew McFedries.
The fight starts off with Drew landing some good punches and just walking through anything Kampmann is throwing. Kampmann's face starts to swell as he gets the fight to the ground. Secures side control and then gets a beautiful arm-triangle and puts McFedries to sleep.
Great fight by Kampmann that shows how a well rounded fighter should always beat a one dimensional fighter.