Molecular fluorescence decay is significantly modified when the emitting molecule is located near a plasmonic structure. When the lateral sizes of such structures are reduced to nanometer-scale cross sections, they can be used to accurately control and amplify the emission rate. In this Rapid Communication, we extend Green's dyadic method to quantitatively investigate both radiative and nonradiative decay channels experienced by a single fluorescent molecule confined in an adjustable dielectric-metal nanogap. The technique produces data in excellent agreement with current experimental work.