Resistive switching (RS) memories have attracted great attention as promising solutions to next-generation non-volatile memories and computing technologies because of their simple device configuration, high on/off ratio, low power consumption, fast switching, long retention, and significant cyclic stability. In this work, uniform and adherent iron tungstate (FeWO4) thin films were synthesized by the spray pyrolysis method with various precursor solution volumes, and these were tested as a switching layer for the fabrication of Ag/FWO/FTO memristive devices. The detailed structural investigation was done through various analytical and physio-chemical characterizations viz. X-ray diffraction (XRD) and its Rietveld refinement, Raman spectroscopy, and X-ray photoelectron spectroscopy (XPS) techniques. The results reveal the pure and single-phase FeWO4 compound thin film formation. Surface morphological study shows the spherical particle formation having a diameter in the range of 20 to 40 nm. The RS characteristics of the Ag/FWO/FTO memristive device demonstrate non-volatile memory characteristics with significant endurance and retention properties. Interestingly, the memory devices show stable and reproducible negative differential resistance (NDR) effects. The in-depth statistical analysis suggests the good operational uniformity of the device. Moreover, the switching voltages of the Ag/FWO/FTO memristive device were modeled using the time series analysis technique by utilizing Holt’s Winter Exponential Smoothing (HWES) approach. Additionally, the device mimics bio-synaptic properties such as potentiation/depression, excitatory post-synaptic current (EPSC), and spike-timing-dependent plasticity (STDP) learning rules. For the present device, the space-charge-limited current (SCLC) and trap-controlled-SCLC effects dominated during positive and negative bias I–V characteristics, respectively. The RS mechanism dominated in the low resistance state (LRS), and the high resistance state (HRS) was explained based on the formation and rupture of conductive filament composed of Ag ions and oxygen vacancies. This work demonstrates the RS in the metal tungstate-based memristive devices and demonstrates a low-cost approach for fabricating memristive devices.