Hepatocellular carcinoma (HCC) is the fifth most common and fatal cancer reported, representing 72.5% of malignancies around the world. The majority of HCC incidents have been associated with infections caused by hepatitis B and C viruses. Many first- and second-line conventional drugs, e.g., sorafenib, cabozantinib, or ramucirumab, have been used for the management of HCC. Despite different combinational therapies, there are still no defined biomarkers for an early stage diagnosis of HCC. The current study evaluated the potential of Bergenia stracheyi, Bergenia ciliata, Bergenia pacumbis, and Bergenia purpurascens, which belong to the family Saxifragaceae, to treat HCC using an integrated network pharmacology and molecular docking approach. Four active phytochemicals were selected based on oral bioavailability (OB) and drug likeness (DL) parameters. The criteria of phytochemical selection were set to OB > 30% and DL > 0.18. Similarly, the gene targets related to Bergenia spp. and the genes related to HCC were retrieved from different databases. The integration of these genes revealed 98 most common overlapping genes, which were mainly interrelated with HCC pathogenesis. Ultimately, the 98 Bergenia-HCC associated genes were used for protein–protein interaction (PPI), Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway, and Gene Ontology (GO) enrichment analyses. Finally, the topological analysis revealed the top ten hub genes with maximum degree rank. From the top ten genes, STAT3, MAPK3, and SRC were selected due to their involvement in GO annotation and KEGG pathway. To confirm the network pharmacology results, molecular docking analysis was performed to target STAT3, MAPK3, and SRC receptor proteins. The phytochemical (+)-catechin 3-gallate exhibited a maximum binding score and strong residue interactions with the active amino acids of MAPK3-binding pockets (S-score: −10.2 kcal/mol), SRC (S-score: −8.9 kcal/mol), and STAT3 (S-score: −8.9 kcal/mol) as receptor proteins. (+)-Catechin 3-gallate and β-sitosterol induced a significant reduction in cell viability in HepG2 after 24 h of treatment in a dose-dependent manner. The results of this study explore the potential of (+)-catechin 3-gallate and β-sitosterol, which can be used in the future as potential drug candidates to suppress HCC.