Supershear earthquake ruptures propagate faster than the shear wave velocity. Although there is evidence that this occurs in nature, it has not been experimentally demonstrated with the use of crustal rocks. We performed stick-slip experiments with Westerly granite under controlled upper-crustal stress conditions. Supershear ruptures systematically occur when the normal stress exceeds 43 megapascals (MPa) with resulting stress drops on the order of 3 to 25 MPa, comparable to the stress drops inferred by seismology for crustal earthquakes. In our experiments, the sub-Rayleigh-to-supershear transition length is a few centimeters at most, suggesting that the rupture of asperities along a fault may propagate locally at supershear velocities. In turn, these sudden accelerations and decelerations could play an important role in the generation of high-frequency radiation and the overall rupture-energy budget.