We report on a population of short-duration near-ultraviolet (NUV) flares in stars observed by the Kepler and Galaxy Evolution Explorer (GALEX) missions. We analyzed the NUV light curves of 34276 stars observed from 2009 to 2013 by both the GALEX (NUV) and Kepler (optical) space missions with the eventual goal of investigating multiwavelength flares. From the GALEX data, we constructed light curves with a 10s cadence, and we ultimately detected 1904 short-duration flares on 1021 stars. The vast majority (94.5%) of these flares have durations less than 5 minutes, with flare flux enhancements above the quiescent flux level ranging from 1.5 to 1700. The flaring stars are primarily solar-like, with Teff ranging from 3000 to 11000K and radii between 0.5 and 15R_{sun}_. This set of flaring stars is almost entirely distinct from that of previous flare surveys of Kepler data and indicates a previously undetected collection of small flares contained within the Kepler sample. The range in flare energies spans 1.8x10^32^-8.9x10^37^erg, with associated relative errors spanning 2%-87%. The flare frequency distribution by energy follows a power law with index {alpha}=1.72+/-0.05, consistent with results of other solar and stellar flare studies at a range of wavelengths. This supports the idea that the NUV flares we observed are governed by the same physical processes present in solar and optical flares. The relationship between flare duration and associated flare energy extends results found for solar and stellar white-light flares, and suggests that these flares originate in regions with magnetic field strengths of several hundred Gauss, and length scales of the order of 10^10^cm.