The EXO-200 experiment searched for neutrinoless double-beta decay of 136Xe with a single-phase liquid xenon detector. It used an active mass of 110 kg of 80.6%-enriched liquid xenon in an ultra-low background time projection chamber with ionization and scintillation detection and readout. This paper describes the design and performance of the various support systems necessary for detector operation, including cryogenics, xenon handling, and controls. Novel features of the system were driven by the need to protect the thin-walled detector chamber containing the liquid xenon, to achieve high chemical purity of the Xe, and to maintain thermal uniformity across the detector.