Bringing together compounds of intrinsically different functionality, such as inorganic nanostructures and organic molecules, constitutes a particularly powerful route to creating novel functional devices with synergetic properties found in neither of the constituents. We introduce nanophotonic functional elements combining two classes of materials, semiconductor nanocrystals and dyes, whose physical nature arises as a superposition of the properties of the individual components. The strongly absorbing rod-like nanocrystals focus the incident radiation by photopumping the weakly absorbing dye via energy transfer. The CdSe/CdS nanorods exhibit a large quantum-confined Stark effect on the single-particle level, which enables direct control of the spectral resonance between donor and acceptor required for nanoscopic Förster-type energy transfer in single nanorod-dye couples. With this far-field manipulation of a near-field phenomenon, the emission from single dye molecules can be controlled electrically. We propose that this effect could lead to the design of single-molecule optoelectronic switches providing building blocks for more complex nanophotonic circuitry.