Chocolate is a widely consumed product, due to the contribution of fats and antioxidant compounds; the addition of other components makes it possible to increase the content of polyunsaturated fatty acids, although they can affect its rheological properties. The influence of the partial addition of peanut paste and Sacha Inchi on the rheological and functional properties of dark chocolate was evaluated. Cocoa beans, peanuts, and Sacha Inchi were refined in order to obtain the cocoa paste (PC), peanut paste (PM), and Sacha Inchi paste (PSI). Then, mixtures between 0 to 20% of PM and PSI were formulated, and the rheological properties were evaluated at 30, 40, and 50 °C; these were adjusted to mathematical models. Functional groups were identified by FTIR in ATR mode, and it was observed that the partial addition of PM and PSI did not show significant changes in the shear stress and apparent viscosity of the mixture, although they did show dependence on temperature. The Herschel–Bulkley model showed a better adjustment (R2 > 0.999), reporting behavior index values, n < 1.0, and indicating pseudo-plastic behavior for pastes and formulations. The yield limit τy and the consistency index kH increased significantly with the addition of PM and PSI, but they decreased with increasing temperature. The activation energy show values between 13.98 to 18.74 kJ/mol, and it increased significantly with the addition of PM and PSI. Infrared analysis evidenced the presence of polyunsaturated fatty acids, coming mainly from PSI and PM. The addition of PM and PSI does not influence the rheological properties and allows for an increase in the content of polyunsaturated fatty acids.