Platinum–dysprosium (Pt–Dy) alloys prepared by the arc melting technique are assessed as potential electrodes for the oxygen reduction reaction (ORR) using voltammetry and chronoamperometry in alkaline media. A relatively small change (10 at.%) in the alloy composition brought a notable difference in the alloys’ performance for the ORR. Pt40Dy60 electrode, i.e., the electrode with a lower amount of Pt, was identified to have a higher activity towards ORR as evidenced by lower overpotential and higher current densities under identical experimental conditions. Furthermore, DFT calculations point out the unique single-atom-like coordination and electronic structure of Pt atoms in the Pt40Dy60 surface as responsible for enhanced ORR activity compared to the alloy with a higher Pt content. Additionally, Pt–Dy alloys showed activity in the oxygen evolution reaction (OER), with the OER current density lower than that of pure Pt.