The areal footprint of memristors is a key consideration in material-based neuromorophic computing and large-scale architecture integration. Electronic transport in the most widely investigated memristive devices is mediated by filaments, posing a challenge to their scalability in architecture implementation. Here we present a compelling alternative memristive device and demonstrate that areal downscaling leads to enhancement in memristive memory window, while maintaining analogue behavior, contrary to expectations. Our device designs directly integrated on semiconducting Nb-SrTiO$_3$ allows leveraging electric field effects at edges, increasing the dynamic range in smaller devices. Our findings are substantiated by studying the microscopic nature of switching using scanning transmission electron microscopy, in different resistive states, revealing an interfacial layer whose physical extent is influenced by applied electric fields. The ability of Nb-SrTiO$_3$ memristors to satisfy hardware and software requirements with downscaling, while significantly enhancing memristive functionalities, makes them strong contenders for non-von Neumann computing, beyond CMOS.