The search for the coexistence between superconductivity and other collective electronic states in many instances promoted the discovery of novel states of matter. The manner in which the different types of electronic order combine remains an ongoing puzzle. 1T-TaS(2) is a layered material, and the only transition-metal dichalcogenide (TMD) known to develop the Mott phase. Here, we show the appearance of a series of low-temperature electronic states in 1T-TaS(2) with pressure: the Mott phase melts into a textured charge-density wave (CDW); superconductivity develops within the CDW state, and survives to very high pressures, insensitive to subsequent disappearance of the CDW state and, surprisingly, also the strong changes in the normal state. This is also the first reported case of superconductivity in a pristine 1T-TMD compound. We demonstrate that superconductivity first develops within the state marked by a commensurability-driven, Coulombically frustrated, electronic phase separation.