High-order harmonics driven by phase- and polarization-structured femtosecond pulses are unique sources of the extreme ultraviolet vortex and vector beams, which have various applications. Here, we report the generation of intense high-order harmonics during propagation of the polarization-structured vector beams (radially polarized beam, azimuthally polarized beam, and their superposition) through the laser-induced plasmas (In, C, CdS, Zns, Ag2S). Low-order harmonics became stronger with radially polarized and azimuthally polarized driving beams compared with the linearly polarized beams, which is explained on the basis of phase matching and specific properties of vector beams. Contrary to that, the resonance-enhanced harmonic generated in the indium plasma in the case of radially polarized and azimuthally polarized beams was twice weaker compared with the harmonic generated by the LP beam due to modification in the resonant transition selection rules leading to a decrease of the oscillator strength of ionic transitions. Harmonic cut-off and intensity in the case of superposition of the radially and azimuthally polarized beams were lesser compared with the cases of the individual (radially polarized and azimuthally polarized) beams.