Precise control of capillary flow is of great importance in open-channel microfluidic technology. We report a compelling strategy to achieve unidirectional liquid flow in open capillary channels. The key flow-rectifying feature is a microfluidic junction between two open channels: a small cross-section, shallower channel, and a large cross-section, deeper channel. Liquids flow from the large channel to the small channel, but flow in the opposite direction is blocked at the junction. Experiments and computational analysis show that rectification follows directly from the Gibbs criterion for flow over step edges. The unidirectional flow behavior is independent of the liquid contact angle and surface tension and also of changes in channel dimensions, suggesting broad applicability for controlling flow. Specifically, we show that the junction structure can be utilized to facilitate the fabrication of electronic devices from functional inks delivered to open capillaries.