Cosmological and astrophysical phenomena indicate the existence of a class of particles that are dark in the sense that they interact only very weakly with the Standard Model (SM). A strong set of candidates are Weakly Interacting Massive Particles (WIMPs) with masses of $m_{\chi}\in10$--$10,000$~GeV. The Large Underground Xenon (LUX) experiment utilized a dual-phase xenon time projection chamber (TPC) to search for this type of dark matter (DM), setting competitive limits on the spin-independent DM-nucleon scattering cross section for $m_{\chi}\gtrsim5$~GeV. It's successor, LUX-ZEPLIN (LZ), is currently being commissioned and will improve upon these results. This dissertation presents work extending the sensitivity of both detectors to rare events above and below the energy range of WIMP scattering. It does so, first, through precise management of backgrounds that can hide or mimic higher-energy signals of interest. A particularly challenging set of backgrounds comes from radon and its daughters. The LUX data were used to characterize the distribution of these isotopes throughout the xenon and place limits on the rate at which radon-related surface contamination washes off of TPC walls. To make this work possible, strategies were developed to accurately calibrate the detector and select high-energy decays by mitigating spurious low-energy signals that accompany the primary events. Another significant source of backgrounds is intrinsic contamination of detector components by primordial nuclides and cosmogenically activated isotopes. To best-design the LZ detector, a new facility named the Black Hills Underground Campus (BHUC) was built to house high-purity germanium (HPGe) detectors. These were used to assays potential construction materials and the lowest-activity materials were selected for use in the LZ detector. In addition, LUX components were assayed to refine the background model of this experiment. This dissertation also presents work lowering the LUX energy threshold to gain sensitivity to low-mass DM. This was done by incorporating events containing only ionization signals which remain robust at very-low energies where there are usually no detectable scintillation signals. In this regime, that data are plagued by backgrounds from radiogenic surface contamination of the grid wires and additional grid electron emissions. A novel machine learning technique was used to mitigate these events based on ionization pulse shape. It was applied to an effective $5$~tonne$\cdot$day exposure from the 2013 LUX science operation to place strong limits on the scattering of low-mass DM particles with $m_{\chi} \in 0.15$--$10$~GeV.