We propose a memristive interface consisting of two FitzHugh–Nagumo electronic neurons connected via a metal–oxide (Au/Zr/ZrO₂(Y)/TiN/Ti) memristive synaptic device. We create a hardware–software complex based on a commercial data acquisition system, which records a signal generated by a presynaptic electronic neuron and transmits it to a postsynaptic neuron through the memristive device. We demonstrate, numerically and experimentally, complex dynamics, including chaos and different types of neural synchronization. The main advantages of our system over similar devices are its simplicity and real-time performance. A change in the amplitude of the presynaptic neurogenerator leads to the potentiation of the memristive device due to the self-tuning of its parameters. This provides an adaptive modulation of the postsynaptic neuron output. The developed memristive interface, due to its stochastic nature, simulates a real synaptic connection, which is very promising for neuroprosthetic applications.