Room-temperature photocurrent measurements in two-dimensional (2D) inorganic-organic perovskite devices reveal that excitons strongly contribute to the photocurrents despite possessing binding energies over 10 times larger than the thermal energies. The p-type (C₆H₉C₂H₄NH₃)₂PbI₄ liberates photocarriers at metallic Schottky aluminum contacts, but incorporating electron- and hole-transport layers enhances the extracted photocurrents by 100-fold. A further 10-fold gain is found when TiO₂ nanoparticles are directly integrated into the perovskite layers, although the 2D exciton semiconducting layers are not significantly disrupted. These results show that strong excitonic materials may be useful as photovoltaic materials despite high exciton binding energies and suggest mechanisms to better understand the photovoltaic properties of the related three-dimensional perovskites.