A novel series of 1,4-naphthoquinones (33–44) tethered by open and closed chain sulfonamide moieties were designed, synthesized and evaluated for their cytotoxic and antimalarial activities. All quinone-sulfonamide derivatives displayed a broad spectrum of cytotoxic activities against all of the tested cancer cell lines including HuCCA-1, HepG2, A549 and MOLT-3. Most quinones (33–36 and 38–43) exerted higher anticancer activity against HepG2 cell than that of the etoposide. The open chain analogs 36 and 42 were shown to be the most potent compounds. Notably, the restricted sulfonamide analog 38 with 6,7-dimethoxy groups exhibited the most potent antimalarial activity (IC$_{50}$ = 2.8 μM). Quantitative structure–activity relationships (QSAR) study was performed to reveal important chemical features governing the biological activities. Five constructed QSAR models provided acceptable predictive performance ($R_{CV}$ 0.5647–0.9317 and RMSEcv 0.1231–0.2825). Four additional sets of structurally modified compounds were generated in silico (34a–34d, 36a–36k, 40a–40d and 42a–42k) in which their activities were predicted using the constructed QSAR models. A comprehensive discussion of the structure–activity relationships was made and a set of promising compounds (i.e., 33, 36, 38, 42, 36d, 36f, 42e, 42g and 42f) was suggested for further development as anticancer and antimalarial agents.