A safe and efficient flow-chemistry-based procedure is presented for 1,3-dipolar cycloaddition reactions between organic azides and acetylenes. This simple and inexpensive technique eliminates the need for costly special apparatus and utilizes Cu powder as a plausible CuI source. To maximize the reaction rates, high-pressure/high-temperature conditions are utilized; alternatively, the harsh reaction conditions can be moderated at room temperature by the joint application of basic and acidic additives. A comparison of the performance of these two approaches in a series of model reactions has resulted in the formation of useful 1,4-disubstituted 1,2,3-triazoles in excellent yields. The risks that are associated with the handling of azides are lowered, thanks to the benefits of flow processing, and gram-scale production has been safely implemented. The synthetic capability of this continuous-flow technique is demonstrated by the efficient syntheses of some highly functionalized derivatives of the antifungal cispentacin.