With the discovery of charge-density waves (CDWs) in most members of the cuprate high-temperature superconductors, the interplay between superconductivity and CDWs has become a key point in the debate on the origin of high-temperature superconductivity. Some experiments in cuprates point toward a CDW state competing with superconductivity, but others raise the possibility of a CDW-superconductivity intertwined order or more elusive pair-density waves (PDWs). Here, we have used proton irradiation to induce disorder in crystals of La1.875Ba0.125CuO₄ and observed a striking 50% increase of T c, accompanied by a suppression of the CDWs. This is in sharp contrast with the behavior expected of a d-wave superconductor, for which both magnetic and nonmagnetic defects should suppress T c. Our results thus make an unambiguous case for the strong detrimental effect of the CDW on bulk superconductivity in La1.875Ba0.125CuO₄. Using tunnel diode oscillator (TDO) measurements, we find indications for potential dynamic layer decoupling in a PDW phase. Our results establish irradiation-induced disorder as a particularly relevant tuning parameter for the many families of superconductors with coexisting density waves, which we demonstrate on superconductors such as the dichalcogenides and Lu₅Ir₄Si10.