Presented are torque converters with integrated engine disconnect devices, methods for making/using such torque converters, and electric-drive vehicles equipped with such torque converters. A torque converter (TC) assembly includes a TC housing that drivingly connects to an engine output member. A TC output member projects from the TC housing and drivingly connects to a transmission input member. A turbine with a bladed turbine shell is mounted on the TC output member and rotatable within the TC's internal fluid chamber. An impeller with a bladed impeller shell is juxtaposed with the turbine and rotatable within the fluid chamber. An engine disconnect device, which is disposed within the fluid chamber between the impeller shell and TC housing, drivingly couples the impeller to and, when desired, drivingly decouples the impeller from the TC housing and engine output member to thereby transfer torque and prevent torque transfer, respectively, between the engine and transmission.