In this Letter, we explain the puzzling sign change of organic magnetoresistance in space-charge limited devices by device physics. We prove analytically and numerically that in the case of bipolar conduction with an Ohmic majority carrier and an injection limited minority carrier contact, a decrease in minority carrier mobility may give rise to an increase in the device current. It is shown that when the magnetic field acts to decrease the mobility of both carriers, a sign change in the magnetoconductivity as a function of applied bias may result. This behavior is in agreement with experimental observations.