I just posted about my yorkies who bark at people who come in our house, so I really don't feel like I'm in the position to hand out advice....but I'm gonna do it anyway
Pippa used to do that same thing...try to dart out the door and was actually successful on a few occasions and thought it was a big game when we started yelling in panic stricken voices and chasing her. She attended obedience school and learned basic obedience, which DID help because she understands the commands "come" and "stay". Now when we leave the house we tell her to "stay" and for the most part she does.
Occasionally she will get a wild hair and go on the lam out the door. She knows it's bad and turns around to see who will chase her. We have outsmarted her by my youngest daughter gleefully calling her name and running toward the backyard clapping her hands. Pippa follows her and I come up the rear and we usually corner her. We try never, ever to run AFTER her-makes her go even faster. So next time, try running AWAY from the puppy and act like you're having the time of your life!!
It's also good to start teaching some basic obedience, then move on to clicker. There's tons of info on the net about clicker training and basic obedience. It just takes lots of patience and treats on your part!