We demonstrate third- (THG) and second-harmonic generation (SHG) microscopy of individual silver nanocones using tightly focused cylindrical vector beams (CVBs). Although THG is expected to be a weaker process than SHG, the yield for THG with radial polarization was higher than for SHG. We also found an excellent correlation between the imaging properties of THG and SHG, suggesting that both are governed by the same overall features of the individual nanocone. We also found that the transverse spatial resolution of THG with CVBs, particularly RP, exceeds that of SHG. Our work establishes the potential of THG microscopy with CVBs for structure-sensitive imaging of three-dimensional (3D) metal nano-objects.