The way to break any zone defense is by getting the ball in the middle of the zone so that the defenders collapse. The problem with a 1-3-1 zone is that they have someone guarding the middle, so getting the ball into the middle can be slightly difficult. The most important man in this offense would be the person in the middle. If that person is not active and aggressive in getting the ball, you are going to be forced to do long passes or dribbling through the zone defense which is exactly what the defense wants you to do.
The point of a 1-3-1 is to meet the dribbler with the top guy in the zone to pester the ball and rush decision making. Once the dribbler gives up the ball, you are met with a wall of defenders in the part of the zone which does two things, either forces traps or passes over the top which the backside guy in the zone is supposed to intercept or pressure. All of this gets nullified if you get the ball to the middle man as the defenders will collapse and open things up down the floor for easier passes. Train the middle man in your zone to be an aggressive zone breaker and handle the pressure that comes when the zone collapses.