Photoelectric heating--heating of dust grains by far-ultraviolet photons--has long been recognized as the primary source of heating for the neutral interstellar medium. Simulations of spiral galaxies have shown some indication that photoelectric heating could suppress star formation; however, simulations that include photoelectric heating have typically shown that it has little effect on the rate of star formation in either spiral galaxies or dwarf galaxies, which suggests that supernovae are responsible for setting the gas depletion time in galaxies. This result is in contrast with recent work indicating that a star formation law that depends on galaxy metallicity--as is expected with photoelectric heating,but not with supernovae--reproduces the present-day galaxy population better than does a metallicity-independent one. Here we report a series of simulations of dwarf galaxies, the class of galaxy in which the effects of both photoelectric heating and supernovae are expected to be strongest. We simultaneously include space and time-dependent photoelectric heating in our simulations, and we resolve the energy-conserving phase of every supernova blast wave, which allows us to directly measure the relative importance of feedback by supernovae and photoelectric heating in suppressing star formation. We find that supernovae are unable to account for the observed large gas depletion times in dwarf galaxies. Instead, photoelectric heating is the dominant means by which dwarf galaxies regulate their star formation rate at any given time,suppressing the rate by more than an order of magnitude relative to simulations with only supernovae.