Metal halide perovskites are promising for memristor applications due to their mixed ionic-electronic nature. We demonstrate that analog memristive behavior can be triggered by careful stoichiometric engineering. Using methylammonium lead iodide (MAPbI_x) devices with the structure ITO/PEDOT:PSS/MAPbI_x/PCBM/Ag, we demonstrate a sharp transition from rectifying to memristive response upon addition of only 2% excess MAI. This memristive behavior is evidenced by substantial inverted hysteresis loops in the I–V sweeps. Impedance spectroscopy reveals a bias-dependent evolution from capacitive to an inductive response, characteristic of slow, history-dependent ionic relaxation. Transient pulsing experiments confirm gradual, analog conductance potentiation on time scales of seconds, consistent with impedance-derived relaxation dynamics. Drift–diffusion simulations attribute the mechanism to reconfiguration of mobile ions and internal electric fields. These results identify stoichiometric control as an effective route to engineer nonfilamentary memristors in halide perovskites, directly linking ionic–electronic coupling to layer composition and enabling energy-efficient analog computing architectures.