Presented are fuel cell systems and control logic for extracting water from system exhaust, methods for making/using such systems, and electric-drive vehicles with aftertreatment systems for extracting water from fuel cell exhaust. An aftertreatment system for a fuel cell stack includes a condensate generator that fluidly connects to the fuel cell stack to receive exhaust output therefrom. The condensate generator includes an evaporator core with a refrigerant line that actively cool the exhaust via controlled circulation of refrigerant fluid. A condensate collector fluidly connected to the condensate generator includes a reservoir housing with a condensate trap that separates entrained water vapor from the cooled exhaust. The reservoir housing collects the separated water vapor as liquid water. A liquid storage container fluidly connected to the condensate collector receives and stores the collected water. An expansion valve regulates the amount of refrigerant fluid passed into the evaporator core through the refrigerant line.