A series of 1,3,4-oxadiazole-1,2,3-triazole hybrids bearing different pharmacophoric moieties has been designed and synthesized. Their antiproliferative activity was evaluated against four human cancer cell lines (Panc-1, MCF-7, HT-29, and A-549) using the MTT (3-(4,5-dimethylthiazol-2-yl)−2,5-diphenyltetrazolium bromide) assay. The preliminary activity test displayed that the most active compounds, 6d, 6e, and 8a–e, suppressed cancer cell growth (GI₅₀ = 0.23–2.00 µM) comparably to erlotinib (GI₅₀ = 0.06 µM). Compounds 6d, 6e, and 8a–e inhibited the epidermal growth factor receptor tyrosine kinase (EGFR-TK) at IC₅₀ = 0.11–0.73 µM, compared to erlotinib (IC₅₀ = 0.08 ± 0.04 µM). The apoptotic mechanism revealed that the most active hybrid 8d induced expression levels of caspase-3, caspase-9, and cytochrome-c in the human cancer cell line Panc-1 by 7.80-, 19.30-, and 13-fold higher than doxorubicin. Also, 8d increased the Bax level by 40-fold than doxorubicin, along with decreasing Bcl-2 levels by 6.3-fold. Cell cycle analysis after treatment of Panc-1 cells with hybrid 8d revealed a high proportion of cell accumulation (41.53%) in the pre-G1 phase, indicating cell cycle arrest at the G1 transition. Computational docking of the 8d and 8e hybrids with the EGFR binding site revealed their ability to bind with EGFR similar to erlotinib. Finally, in silico absorption, distribution, metabolism, and excretion/pharmacokinetic studies for the most active hybrids are discussed.