The interactions between tannins and soluble and insoluble cell wall components are, in part, responsible for the low quantities of tannins found in wines compared with the quantities in grapes. The use of polysaccharides to compete with cell wall components could be an interesting approach for improving the chromatic and sensory characteristics of wines. The effect of two commercial polysaccharides, pectin and mannan, on limiting tannin-cell wall interactions was studied in a model solution, measuring the concentration of tannins and polysaccharides remaining in solution after the different interactions by chromatography. The treatment was also tested in a small-scale vinification. Soluble polysaccharides were added to the must and the wines were evaluated at the end of alcoholic fermentation and after six months in the bottle. In the model solution, the commercial polysaccharides formed soluble complexes with the tannins and limited the interactions with cell wall components, with some differences between skin and seed tannins. In the case of the wines, the treatments resulted in wines with a higher color intensity and phenolic content. Sensory analysis resulted in higher scores for the wines with added polysaccharides, since the complexation of tannins with the polysaccharides increased the roundness and body of the resulting wines.