The present invention is directed to a method for sensing the resistance state of a memory cell that includes an MTJ memory element coupled to a two-terminal selector element in series. The method includes the steps of raising a cell voltage across the memory cell above a threshold voltage for the selector element to become conductive; decreasing the cell voltage to a first sensing voltage and measuring a first sensing current passing through the memory cell, the selector element being nominally conductive irrespective of the resistance state of the MTJ memory element at the first sensing voltage; and further decreasing the cell voltage to a second sensing voltage and measuring a second sensing current, the selector element being nominally conductive if the MTJ memory element is in the low resistance state or nominally insulative if the MTJ memory element is in the high resistance state at the second sensing voltage.