In this study, we first focused on measuring H₂S and oxidative stress as indicators of in-hospital mortality observed within 24 h from admission in hospitalized non-survivor and survivor patients affected by COVID-19. Then, we analyzed whether N-acetylcysteine (NAC) can increase H₂S and GSH concentrations in different cell lines. H₂S levels were significantly increased in all COVID-19 patients (both survivors and non-survivors) compared to non-COVID-19 subjects (p = 0.0016), but non-survivors showed significantly lower H₂S plasma levels than survivors (p = 0.008). Oxidative stress measured as circulating malondialdehyde (MDA) resulted in lower levels in non-COVID-19 subjects than in the two COVID-19 patient groups (p = 0.03). However, non-survivors had significantly higher plasma MDA than survivors (p = 0.0001). A Kaplan–Meier curve for H₂S indicates a markedly reduced survival probability in COVID-19 patients with lower H₂S levels (log-rank p = 0.004). NAC activity significantly reduced reactive oxygen species and lipid peroxidation induced by tert-butyl hydroperoxide in cultured cells (p from <0.01 to <0.001). Furthermore, NAC increased the cellular production of H₂S (p < 0.01) and GSH (p < 0.01). These findings indicate the important prognostic role of H₂S in COVID-19 patients at hospital admission and that NAC might be helpful in all clinical situations characterized by low levels of H₂S.