This work presents a flexible synthesis of 10 novel naphthoquinone-chalcone derivatives (1-10) by nucleophilic substitution of readily accessible aminochalcones and 2,3-dichloro-1,4-naphthoquinone. All compounds displayed broad-spectrum cytotoxic activities against all the tested cancer cell lines (i.e., HuCCA-1, HepG2, A549, MOLT-3, T47D, and MDA-MB-231) with IC50 values in the range of 0.81-62.06 μM, especially the four most potent compounds 1, 3, 8, and 9. The in vitro investigation on the fibroblast growth factor receptor 1 (FGFR1) inhibitory effect indicated that eight derivatives (1-2, 4-5, and 7-10) were active FGFR1 inhibitors (IC50 = 0.33-3.13 nM) with more potency than that of the known FGFR1 inhibitor, AZD4547 (IC50 = 12.17 nM). Promisingly, compounds 5 (IC50 = 0.33 ± 0.01 nM), 9 (IC50 = 0.50 ± 0.04 nM), and 7 (IC50 = 0.85 ± 0.08 nM) were the three most potent FGFR1 inhibitors. Molecular docking, molecular dynamics simulations, and MM/GBSA-based free energy calculation revealed that the key amino acid residues involved in the binding of the compounds 5, 7, and 9 and the target FGFR1 protein were similar with those of the AZD4547 (i.e., Val492, Lys514, Ile545, Val561, Ala640, and Asp641). These findings revealed that the newly synthesized naphthoquinone-chalcone scaffold is a promising structural feature for an efficient inhibition of FGFR1.