Molecular vibrations have oscillation periods that reflect the molecular structure, and are hence being used as a spectroscopic fingerprint for detection and identification. At present, all nonlinear spectroscopy schemes use two or more laser beams to measure such vibrations. The availability of ultrashort (femtosecond) optical pulses with durations shorter than typical molecular vibration periods has enabled the coherent excitation of molecular vibrations using a single pulse. Here we perform single-pulse vibrational spectroscopy on several molecules in the liquid phase, where both the excitation and the readout processes are performed by the same pulse. The main difficulty with single-pulse spectroscopy is that all vibrational levels with energies within the pulse bandwidth are excited. We achieve high spectral resolution, nearly two orders of magnitude better than the pulse bandwidth, by using quantum coherent control techniques. By appropriately modulating the spectral phase of the pulse we are able to exploit the quantum interference between multiple paths to selectively populate a given vibrational level, and to probe this population using the same pulse. This scheme, using a single broadband laser source, is particularly attractive for nonlinear microscopy applications, as we demonstrate by constructing a coherent anti-Stokes Raman (CARS) microscope operating with a single laser beam.