Porphyry copper deposits are important sources of copper and typically processed by flotation to produce copper concentrates. As mining areas become deeper, the amounts of impurities, such as sphalerite, can be increased in copper ores, so the appropriate depression of sphalerite floatability should be achieved to obtain saleable copper concentrates. In this study, the flotation behaviors of chalcopyrite and sphalerite in model samples mimicking copper ores with high Cu/Zn ratios (i.e., the ratio of chalcopyrite/sphalerite = 13:1) were investigated with zinc sulfate as a depressant for sphalerite. In addition, the effect of pyrite—a major gangue mineral in copper ores—on the depression of sphalerite floatability with zinc sulfate was examined. When sphalerite and chalcopyrite coexisted, the floatability of the former was effectively depressed by zinc sulfate (Zn recovery: <12%), whereas the presence of pyrite promoted the release of Cu2+ due to the galvanic interaction with chalcopyrite, which resulted in the elimination of the effectiveness of zinc sulfate in depressing sphalerite floatability (Zn recovery: >90%). Despite the presence of much higher amounts of chalcopyrite and pyrite than sphalerite, the application of nitrogen (N2) gas limiting the galvanic interaction between pyrite and chalcopyrite by reducing the dissolved oxygen (DO) concentration in the system effectively depressed the floatability of sphalerite (Zn recovery: <30%).