Elastic waves have been observed to increase productivity of oil wells, although the reason for the vibratory mobilization of the residual organic fluids has remained unclear. Residual oil is entrapped as ganglia in pore constrictions because of resisting capillary forces. An external pressure gradient exceeding an unplugging threshold is needed to carry the ganglia through. The vibrations help overcome this resistance by adding an oscillatory inertial forcing to the external gradient; when the vibratory forcing acts along the gradient and the threshold is exceeded, instant unplugging occurs. The mobilization effect is proportional to the amplitude and inversely proportional to the frequency of vibrations. We observe this dependence in a laboratory experiment, in which residual saturation is created in a glass micromodel, and mobilization of the dyed organic ganglia is monitored using digital photography. We also directly demonstrate the release of an entrapped ganglion by vibrations in a computational fluid-dynamics simulation.