The objective of this work is to develop a novel laser-excited spectrometric method to reliably detect a single molecule in a flowing stream which is confined in a capillary. An argon ion-pumped Ti-sapphire laser tuned to a rubidium atomic transition line at 780.023 nn is used to excite the fluorescence of IR140 molecules in a capillary. A focused laser beam illuminates the whole capillary inner diameter to achieve near unity spatial probing efficiency. A rubidium metal vapor filter, based on the resonance absorption of an atomic metal vapor, absorbs the laser specular scatter from the capillary while passing the molecular fluorescence. The photoelectron signal is measured during the transit time of a single molecule through the 1.05-pL probe volume. A digital weighted quadratic summing filter is used to extract the individual photon bursts from single molecules. The measurement efficiency for the near-infrared dye IR140 is estimated to be near unity. The average number of photoelectrons from a single IR140 molecule is estimated to be 5.9, 7.0, and 8.5 for laser powers of 50, 100, and 150 mW, respectively.