We used classical linear and microwave-assisted synthesis methods to prepare novel N-substituted, benzimidazole-derived acrylonitriles with antiproliferative activity against several cancer cells in vitro. The most potent systems showed pronounced activity against all tested hematological cancer cell lines, with favorable selectivity towards normal cells. The selection of lead compounds was also tested in vitro for tubulin polymerization inhibition as a possible mechanism of biological action. A combination of docking and molecular dynamics simulations confirmed the suitability of the employed organic skeleton for the design of antitumor drugs and demonstrated that their biological activity relies on binding to the colchicine binding site in tubulin. In addition, it also underlined that higher tubulin affinities are linked with (i) bulkier alkyl and aryl moieties on the benzimidazole nitrogen and (ii) electron-donating substituents on the phenyl group that allow deeper entrance into the hydrophobic pocket within the tubulin’s β-subunit, consisting of Leu255, Leu248, Met259, Ala354, and Ile378 residues.