SARS-CoV-2 infection generates approximately one million virions per day, and the majority of available antivirals are ineffective against it due to the virus's inherent genetic mutability. This necessitates the investigation of concurrent inhibition of multiple SARS-CoV-2 targets. We show that fortunellin (acacetin 7-O-neohesperidoside), a phytochemical, is a promising candidate for preventing and treating COVID-19 and SARS by targeting multiple key viral target proteins, supporting protective immunity while inhibiting pro-inflammatory cytokines and apoptosis pathways, and protecting against tissue damage. Fortunellin is a phytochemical found in Gojihwadi Kwath, an Indian traditional Ayurvedic formulation with antiviral activity that has been shown to be effective in COVID-19 patients. The mechanistic action of its antiviral activity, however, is unknown. The current study comprehensively evaluates the potential therapeutic mechanisms of fortunellin in preventing and treating COVID-19 using molecular docking, molecular dynamics simulations, free-energy calculations, host target mining of fortunellin, gene ontology enrichment, pathway analyses, and protein-protein interaction analysis. Using computational approaches, we show that fortunellin reliably binds to key targets that are necessary for viral replication, growth, invasion, and infectivity, including Nucleocapsid (N-CTD) (-51.30 kcal/mol) and Replicase-dimer ( -45.91 kcal/mol), Replicase-monomer-NSP-8 binding site (-29.9 kcal/mol), Papain-like-protease (-29.60 kcal/mol), Nucleocapsid-NTD (28.46 kcal/mol), 2’-O-methyltransferase (-24.33 kcal/mol), Main-protease (-23.48 kcal/mol), Spike-RBD (-23.3 kcal/mol), Replicase-monomer at dimer interface (-23.27) kcal/mol, RNA-dependent-RNA-polymerase (-14.24 kcal/mol). Furthermore, we identify and evaluate the potential human targets of fortunellin and its effect on the SARS-CoV-2 infected tissues, including normal-human-bronchial-epithelium and lung cells, and organoids such as pancreatic, colon, liver, and cornea, using a computational network pharmacology approach. Thus, our findings indicate that fortunellin has a dual role: multi-target antiviral activities against SARS-CoV-2, as well as immunomodulatory capabilities against the host. In the future, lab-based and clinical studies will be required.