Digital microfluidics (DMF) is a powerful technique for sample preparation and analysis for a broad range of biological and chemical applications. In many cases, it is desirable to carry out DMF on an open surface, such that the matrix surrounding the droplets is ambient air. However, the utility of the air-matrix DMF format has been severely limited by problems with droplet evaporation, especially when the droplet-based biochemical reactions require high temperatures for long periods of time. We present a simple solution for managing evaporation in air-matrix DMF: just-in-time replenishment of the reaction volume using droplets of solvent. We demonstrate that this solution enables DMF-mediated execution of several different biochemical reactions (RNA fragmentation, first-strand cDNA synthesis, and PCR) over a range of temperatures (4-95°C) and incubation times (up to 1 h or more) without use of oil, humidifying chambers, or off-chip heating modules. Reaction volumes and temperatures were maintained roughly constant over the course of each experiment, such that the reaction kinetics and products generated by the air-matrix DMF device were comparable to those of conventional benchscale reactions. This simple yet effective solution for evaporation management is an important advance in developing air-matrix DMF for a wide variety of new, high-impact applications, particularly in the biomedical sciences.