The majority of basaltic magmas stall in the Earth’s crust as a result of the rheological evolution caused by crystallization during transport. However, the relationships between crystallinity, rheology and eruptibility remain uncertain because it is difficult to observe dynamic magma crystallization in real time. Here, we present in-situ 4D data for crystal growth kinetics and the textural evolution of pyroxene during crystallization of trachybasaltic magmas in high-temperature experiments under water-saturated conditions at crustal pressures. We observe dendritic growth of pyroxene on initially euhedral cores, and a surprisingly rapid increase in crystal fraction and aspect ratio at undercooling ≥30 °C. Rapid dendritic crystallization favours a rheological transition from Newtonian to non-Newtonian behaviour within minutes. We use a numerical model to quantify the impact of rapid dendritic crystallization on basaltic dike propagation, and demonstrate its dramatic effect on magma mobility and eruptibility. Our results provide insights into the processes that control whether intrusions lead to eruption or not.