The ongoing epidemic caused by SARS-CoV-2 infection led to the search for fundamentally new ways and means to combat inflammation and other pathologies caused by this virus. Using a cellular model of lipopolysaccharide (LPS)-induced sepsis (human promonocytes), we showed that both a hydrogen sulfide donor (sodium thiosulfate, STS) and a recombinant Heat shock protein 70 (rHsp70) effectively block all major inflammatory mediators when administrated before and after LPS challenge. The protective anti-inflammatory effect of rHsp70 and H2S was also confirmed in vivo using various animal models of pneumonia. Specifically, it was found that rHsp70 injections prevented the development of the acute respiratory distress syndrome in highly pathogenic pneumonia in mice, increased animal survival, and reduced the number of Programmed death-1 (PD-1)-positive T-lymphocytes in peripheral blood. Based on our model experiments we developed a combined two-phase therapeutic approach for the treatment of COVID-19 patients. This procedure includes the inhalation of hot helium–oxygen mixtures for induction of endogenous Hsp70 in the first phase and STS inhalation in the second phase. The use of this approach has yielded positive results in COVID-19 patients, reducing the area of lung lesions, restoring parameters of innate immunity and T-cell immune response against coronavirus infection, and preventing the development of pulmonary fibrosis and immune exhaustion syndrome.