Modern power delivery systems are rapidly evolving with high proliferation of power-electronic (PE)-interfaced distributed energy resources (DERs). Compared to the conventional sources of generation, the PE-interfaced DERs, e.g., solar and wind resources, are attributed substantially different characteristics such as lower overload capability and limited frequency response patterns. This paper focuses on effective management and control mechanisms for PE-interfaced DERs in power distribution systems with high penetration of renewables, particularly under fault, voltage-sag, load variations, and other prevailing conditions in the grid. Aiming at the solutions to enhance the system performance resilience, we introduce an advanced model predictive control (MPC) based scheme to control the DER units, minimize the impact of transients and disruptions, speed up the response and recovery of particular metrics and parameters, and maintain an acceptable operation condition. The performance of the suggested control scheme is tested on a modified IEEE 34-bus test feeder, where the proposed solution demonstrates its effectiveness to minimize the system transient during faults, with an enhanced grid-edge and system-wide resilience characteristics in voltage profiles.