The objects of the present invention are to provide a new technology platform for quantitation number of copies of nucleic acid molecules of interest by lumonogenic (i.e., enzymatic luminescence) detection. The detection approach of the method of present invention is essentially employing time-resolved approach, e.g., based on detection transient parameters of luminescent signal. The various disclosed embodiments allow DNA and RNA quantification in a broad dynamic range; can be used for detection of DNA, as well as long (mRNA) and short (microRNA) RNA targets. The present invention provides methods, instruments, and kits for fast and highly sensitive identification and measurements of nucleic acids in various life science and biomedical applications.