This work aimed to develop oil-in-water emulsion gels based on quinoa protein or quinoa protein hydrolysates, alginate, and high-oleic sunflower oil and to characterize their potential as functional food ingredients with antioxidant capacity. Quinoa protein concentrate (QPC) was hydrolyzed with alcalase. The resulting quinoa protein hydrolysates (QPH) (DH: 30 ± 4%) were evaluated for their iron-chelating activity and reducing power. The antioxidant capacity of the QPC or QPH-based emulsion gels was determined using the ABTS and DPPH methods, and they were also subjected to rheological analysis. The QPH exhibited higher ability to chelate ferrous ions and higher reducing power compared to QPC (p = 0.004; p < 0.000, respectively). The ABTS and DPPH free radical scavenging activity of QPH-based emulsion gels was higher than that obtained from QPC-based emulsion gels (p = 0.001; p = 0.001). Furthermore, QPH proved to be more effective in depressing lipid oxidation than QPC. After 30 days of storage, QPH-based emulsion gels showed lower levels of malondialdehyde compared to those obtained from QPC-based emulsion gels (p < 0.000). The rheological behavior of the emulsion gels revealed that the storage modulus (Gʹ) was greater than the loss modulus (Gʺ) throughout the entire frequency range, thus deformation in the linear region was mainly elastic. The strain recovery occurred because of the good viscoelastic properties of the samples. Although the strengthening of QPH-based emulsion gels was lesser than that of those with QPC, the gel structure remained stable through the entire temperature range.