When you shoot a zombie down, linger an extra moment to make sure a pool of blood forms around the fallen monster. Sometimes they will simply fall and lay there, waiting for you to pass so they can grab you. If you do not see a pool of blood, shoot some extra rounds from your weapon. Also, sometimes you will see a fallen zombie that appears dead, but you have not shot. They might not be dead. Shoot them once to be sure. If they spring up, finish them off before they finish you.