We demonstrate a unique parameter for biomolecule separation that results from the nonlinear response of long, charged polymers to electrophoretic fields and apply it to extraction and concentration of nucleic acids from samples that perform poorly under conventional methods. Our method is based on superposition of synchronous, time-varying electrophoretic fields, which can generate net drift of charged molecules even when the time-averaged molecule displacement generated by each field individually is zero. Such drift can only occur for molecules, such as DNA, whose motive response to electrophoretic fields is nonlinear. Consequently, we are able to concentrate DNA while rejecting high concentrations of contaminants. We demonstrate one application of this method by extracting DNA from challenging samples originating in the Athabasca oil sands.