The present invention is directed to methods of detecting nucleic acids in a biological sample. The method is based on a novel combination of a base extension reaction, which provides excellent analytical specificity, and a mass spectrometric analysis, which provides excellent specificity. The method can be used, for example, for diagnostic, prognostic and treatment purposes. The method allows accurate detection of nucleic acids that are present in very small amounts in a biological sample. For example, the method of the present invention is preferably used to detect fetal nucleic acid in a maternal blood sample; circulating tumor-specific nucleic acids in a blood, urine or stool sample; and donor-specific nucleic acids in transplant recipients. In another embodiment, one can detect viral, bacterial, fungal, or other foreign nucleic acids in a biological sample.