This article deals with the stochastic resonance (SR) phenomenon experimentally observed in HfO2-based memristors. The SR impact on the binary spike time-dependent plasticity (STDP) protocol at the device level was investigated. We demonstrate that the two extreme conductance states of the device that represent the synaptic weights in neuromorphic systems can be better distinguished with the incorporation of Gaussian noise into the bias signal. This technique allows setting the memristor conductance which is directly related to the overlap between the pre- and postsynaptic pulses. The study is reproduced in the LTSPICE simulator using the dynamic memdiode model (DMM) for memristors.