The number of people affected by cancer and antibiotic-resistant bacterial infections has increased, such that both diseases are already seen as current and future leading causes of death globally. To address this issue, based on a combined in silico and in vitro approach, we explored the anticancer potential of known antibacterials with a thiazolidinedione–thiosemicarbazone (TZD–TSC) core structure. A cytotoxicity assessment showed encouraging results for compounds 2–4, with IC50 values against T98G and HepG2 cells in the low micromolar range. TZD–TSC 3 proved to be most toxic to cancer cell lines, with IC50 values of 2.97 ± 0.39 µM against human hepatoma HepG2 cells and IC50 values of 28.34 ± 2.21 µM against human glioblastoma T98G cells. Additionally, compound 3 induced apoptosis and showed no specific hemolytic activity. Furthermore, treatment using 3 on cancer cell lines alters these cells’ morphology and further suppresses migratory activity. Molecular docking, in turn, suggests that 3 would have the capacity to simultaneously target HDACs and PPARγ, by the activation of PPARγ and the inhibition of both HDAC4 and HDAC8. Thus, the promising preliminary results obtained with TZD–TSC 3 represent an encouraging starting point for the rational design of novel chemotherapeutics with dual antibacterial and anticancer activities.