In the past 2 years, the coronavirus disease 2019 (COVID-19) pandemic has driven investigational studies and controlled clinical trials on antiviral treatments and vaccines that have undergone regulatory approval. Now that the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and its variants may become endemic over time, there remains a need to identify drugs that treat the symptoms of COVID-19 and prevent progression toward severe cases, hospitalization, and death. Understanding the molecular mechanisms of SARS-CoV-2 infection is extremely important for the development of effective therapies against COVID-19. This review outlines the key pathways involved in the host response to SARS-CoV-2 infection and discusses the potential role of antioxidant and anti-inflammatory pharmacological approaches for the management of early mild-to-moderate COVID-19, using the examples of combined indomethacin, low-dose aspirin, omeprazole, hesperidin, quercetin, and vitamin C. The pharmacological targets of these substances are described here for their possible synergism in counteracting SARS-CoV-2 replication and progression of the infection from the upper respiratory airways to the blood, avoiding vascular complications and cytokine and bradykinin storms.