In this study, an alternative and efficient one-pot three-component synthesis approach to develop a new series of (E)-2-aryl-4-styrylquinazolines and (E)-4-styrylquinazolines is described. According to this approach, the target compounds were synthesized straightforward in high yields and in short reaction times from substituted 1-(2-aminophenyl)-3-arylprop-2-en-1-ones via its well-Cu(OAc)2-mediated cyclocondensation reactions with aromatic aldehydes or its well-catalyst-free cyclocondensation reactions with trimethoxy methane (trimethyl orthoformate), and ammonium acetate under aerobic conditions. This is an operationally simple, valuable, and direct method to synthesize 2-aryl- and non-C2-substituted quinazolines containing a styryl framework at C4 position from cheap and synthetically available starting materials. All the synthesized compounds were submitted to the US National Cancer Institute for in vitro screening. The bromo- and chloro-substituted quinazolines 5c and 5d displayed a potent antitumor activity against all the tested subpanel tumor cell lines with IC50 (MG-MID) values of 5.25 and 5.50 μM, and a low cytotoxic effect with LC50 (MG-MID) values of 91.20 and 84.67 μM, respectively, indicating a low toxicity of these compounds to normal human cell lines, as required for potential antitumor agents.