Well in earthbound, you see the enemy on the map much like Chrono Trigger, there are no random battles. What I mean is, if the enemy is looking away and you touch the enemy's back, you will get to attack first (a surprise attack).
However in the second case, if the enemy is a lower level then you, they will try to run away from you and you have catch them to instant kill them, this can be done with or without a surprise attack.
I know in some rpgs with random battles, enemies will puss out and run away, DDS1/2 taught me this well. But Earthbound is way old, and the pioneer, is what I'm saying. Most of the games you mentioned are 3d thus probably not as old as earthbound anyway.