We report on a theoretical analysis and experimental verification of a mechanism for photoconductance, the change in conductance upon illumination, in symmetric single-molecule junctions. We demonstrate that photoconductance at resonant illumination arises due to the Coulomb interaction between the electrons and holes in the molecular bridge, so-called exciton-binding. Using a scanning tunneling microscopy break junction technique, we measure the conductance histograms of perylene tetracarboxylic diimide (PTCDI) molecules attached to Au-electrodes, in the dark and under illumination, and show a significant and reversible change in conductance, as expected from the theory. Finally, we show how our description of the photoconductance leads to a simple design principle for enhancing the performance of molecular switches.