We present a novel analysis technique for liquid xenon time projection chambers that allows for a lower threshold by relying on events with a prompt scintillation signal consisting of single detected photons. The energy threshold of the LUX dark matter experiment is primarily determined by the smallest scintillation response detectable, which previously required a 2-fold coincidence signal in its photomultiplier arrays, enforced in data analysis. The technique presented here exploits the double photoelectron emission effect observed in some photomultiplier models at vacuum ultraviolet wavelengths. We demonstrate this analysis using an electron recoil calibration dataset and place new constraints on the spin-independent scattering cross section of weakly interacting massive particles (WIMPs) down to 2.5 GeV/c2 WIMP mass using the 2013 LUX dataset. This new technique is promising to enhance light WIMP and astrophysical neutrino searches in next-generation liquid xenon experiments.