Detection of excited electronic-ground-state hydrogen molecules with v(") up to 13 in a magnetic multipole plasma source was performed for the first time by laser-induced fluorescence with vacuum-ultraviolet radiation. The measurements are taken after fast shutoff of the discharge current. The rovibrationally excited molecules live longer than the plasma background light so that the fluorescence light can be detected with good signal-to-noise ratio. Absolute level populations are measured as well as decay times. The theoretically predicted suprathermal population of the vibrational distribution is clearly identified. The H- density is calculated on the basis of the measured populations and the measured electron energy distribution function. It is in excellent agreement with the H- density measured by photodetachment.