Drilling hydrocarbon formations where hydrogen sulfide (H2S) is present could lead to the carryover of H2S with the drilling mud (i.e., drilling fluid) to the surface, exposing working personnel to this lethal gas. Additionally, H2S is very corrosive, causing severe corrosion of metal parts of the drilling equipment, which in turn results in serious operational problems. The addition of an effective H2S scavenger(s) in the drilling mud formulations will overcome these health, safety, and operational issues. In this work, zinc oxide (ZnO), which is a common H2S scavenger, has been incorporated into water-based drilling mud. The H2S scavenging performance of this ZnO-containing drilling mud has been assessed. Additionally, drilling mud formulations containing either copper nitrate (Cu(NO3)2·3H2O) or potassium permanganate (KMnO4) have been prepared, and their H2S scavenging performances have been studied and compared to that of the ZnO-containing drilling mud. It has been observed that the scavenging performance (in terms of the H2S amounts scavenged up to the breakthrough time and at the saturation condition) of the ZnO-containing drilling mud is very poor compared to those of the copper nitrate-containing and KMnO4-containing drilling muds. For instance, the amounts of H2S scavenged up to the breakthrough time by ZnO-containing, copper nitrate-containing, and KMnO4-containing drilling muds were 5.5, 15.8, and 125.3 mg/g, respectively. Furthermore, the amounts of H2S scavenged at the saturation condition by these drilling muds were, respectively, 35.1, 146.8, and 307.5 mg/g, demonstrating the superiority of the KMnO4-containing drilling mud. Besides its attractive H2S scavenging performance, the KMnO4-containing drilling mud possessed more favorable rheological properties [i.e., plastic viscosity (PV), yield point (YP), carrying capacity of the drill cuttings, and gelling characteristics] relative to the base and the ZnO-containing and copper nitrate-containing drilling muds. The addition of KMnO4 to the base drilling mud increased its apparent viscosity, PV, and YP by 20, 33, and 10%, respectively. Additionally, all tested drilling muds possessed acceptable fluid loss characteristics. To the best of our knowledge, there are so far no published studies concurrently tackling the H2S scavenging (i.e., breakthrough time, breakthrough capacity, saturation time, saturation capacity, and scavenger utilization) and the rheological properties of water-based drilling muds, as demonstrated in the current study, highlighting the novelty of this work.