The excitation of a fullerene-cage vibrational mode by inelastic tunneling electrons has been observed on single C-60 molecules adsorbed on Ag(110). The vibration is assigned to the H-g(omega(2)) mode. A critical enhancement of the inelastic signal was found on fullerenes oriented along one of their symmetry axis upon adsorption. In strong coincidence, those fullerenes maintain a resonance structure at the Fermi level that resembles the first unoccupied molecular orbital distribution of a free molecule, as determined by comparison with ab initio calculations. The degree of symmetry of the adsorbed fullerene is found to be crucial for resonant mechanism of vibrational excitation. We also propose that mode degeneracy splitting may reduce mode detection.