When a Mott metal-insulator transition is inhibited by a small amount of disorder in the layered dichalcogenide 1T-TaS2, an inhomogeneous superconducting state arises below T=2.1 K and coexists with a nearly commensurate charge-density wave. By angle-resolved photoelectron spectroscopy, we show that it emerges from a bad metal state with strongly damped quasiparticles. Superconductivity is almost entirely suppressed by an external magnetic field of 0.1 T.