During moonlit nights, observations with ground-based Cherenkov telescopes atvery high energies (VHE, $E>100$ GeV) are constrained since the photomultipliertubes (PMTs) in the telescope camera are extremely sensitive to the backgroundmoonlight. Observations with the VERITAS telescopes in the standardconfiguration are performed only with a moon illumination less than 35$\%$ offull moon. Since 2012, the VERITAS collaboration has implemented a newobserving mode under bright moonlight, by either reducing the voltage appliedto the PMTs (reduced-high-voltage configuration, RHV), or by utilizingUV-transparent filters. While these operating modes result in lower sensitivityand increased energy thresholds, the extension of the available observing timeis useful for monitoring variable sources such as blazars and sources requiringspectral measurements at the highest energies. In this paper we report thedetection of $\gamma$-ray flaring activity from the BL Lac object 1ES 1727+502during RHV observations. This detection represents the first evidence of VHEvariability from this blazar. The integral flux is$(1.1\pm0.2)\times10^{-11}\mathrm{cm^{-2}s^{-1}}$ above 250 GeV, which is aboutfive times higher than the low-flux state. The detection triggered additional\veritas\ observations during standard dark-time. Multiwavelength observationswith the FLWO 48" telescope, and the Swift and Fermi satellites are presentedand used to produce the first spectral energy distribution (SED) of this objectduring $\gamma$-ray flaring activity. The SED is then fitted with a standardsynchrotron-self-Compton model, placing constraints on the properties of theemitting region and of the acceleration mechanism at the origin of therelativistic particle population in the jet.