Glycerol is a co-solvent for water extraction that has been shown to be highly effective for obtaining polyphenol extracts under atmospheric conditions. However, its efficacy under subcritical conditions has not yet been studied. We assessed different water-glycerol mixtures (15%, 32.5%, and 50%) in a hot pressurized liquid extraction system (HPLE: 10 MPa) at 90 °C, 120 °C, and 150 °C to obtain extracts of low molecular weight polyphenols from Carménère grape pomace. Under the same extraction conditions, glycerol as a co-solvent achieved significantly higher yields in polyphenols than ethanol. Optimal extraction conditions were 150 °C, with 32.5% glycerol for flavonols and 50% for flavanols, stilbenes, and phenolic acids. Considering gallic acid as a model molecule, computational chemistry calculations were applied to explain some unusual extraction outcomes. Furthermore, glycerol, methanol, ethanol, and ethylene glycol were studied to establish an incipient structure–property relationship. The high extraction yields of gallic acid obtained with water and glycerol solvent mixtures can be explained not only by the additional hydrogen bonds between glycerol and gallic acid as compared with the other alcohols, but also because the third hydroxyl group allows the formation of a three-centered hydrogen bond, which intensifies the strongest glycerol and gallic acid hydrogen bond. The above occurs both in neutral and deprotonated gallic acid. Consequently, glycerol confers to the extraction solvent a higher solvation energy of polyphenols than ethanol.