Delaying mitotic cell cycle progression has been proposed as a strategy to potentiate the effects of anti-mitotic anti-cancer drugs that induce multipolar mitotic spindles. Toward this end, we have performed an in silico docking screen targeting anaphase-promoting complex/cyclosome subunit 1 (APC1) at a conserved 10-amino acid surface site that was modeled to interact via a single hydrogen bond with the essential mitotic anaphase-promoting complex/cyclosome (APC/C) co-factor cell division cycle 20 (CDC20). Five molecules were identified after screening 15,000 small molecules. As a secondary in cellulo bioactivity screening, MDA-MB-231 genomically unstable aneuploid breast cancer cells were exposed to each compound in the absence and presence of 10 nM paclitaxel or 1 nM eribulin, the likely clinically relevant doses of these drugs in these cells. Two of the five compounds, which share a common 2-(trifluoromethyl)quinazolin-4-amine chemical structure, induced elevated levels of cell death in combination with paclitaxel, as observed by fluorescence-activated cell sorting (FACS). These two compounds will now serve as a starting point for further optimization and target validation experiments and for additional in silico screens in search of other chemically related small molecules that display more potent but specific anti-cancer cell effects.