Recent evidence suggests that fibrotic liver injury in patients with chronic hepatitis C correlates with cellular senescence in damaged liver tissue. However, it is still unclear how senescence can affect replication of the hepatitis C virus (HCV). In this work, we report that an inhibitor of cyclin-dependent kinases 4/6, palbociclib, not only induced in hepatoma cells a pre-senescent cellular phenotype, including G1 arrest in the cell cycle, but also accelerated viral replicon multiplication. Importantly, suppression of HCV replication by direct acting antivirals (DAAs) was barely affected by pre-senescence induction, and vice versa, the antiviral activities of host-targeting agents (HTAs), such as inhibitors of human histone deacetylases (HDACi), produced a wide range of reactions—from a dramatic reduction to a noticeable increase. It is very likely that under conditions of the G1 arrest in the cell cycle, HDACi exhibit their actual antiviral potency, since their inherent anticancer activity that complicates the interpretation of test results is minimized.