A fuel-fired water heater has a single pass condensing-type heat exchanger disposed within its water storage tank portion. The heat exchanger includes a primary non-condensing portion defined by a combustion chamber positioned in an upper interior portion of the tank and having a spaced series of vertical tubes depending therefrom. A secondary condensing portion of the heat exchanger is defined by a plenum having a top side connected to the bottom ends of the vertical tubes, and a bottom side from which a downwardly coiled flue tube depends. A fuel burner generates hot combustion gases that are sequentially flowed into the combustion chamber and then downwardly through the balance of the heat exchanger in a single pass.