Palladium catalysts were obtained by the adsorption method involving the sequential deposition of polyvinylpyrrolidone (PVP) and then palladium ions on a modified zinc oxide surface without high-temperature calcination and reduction stages. The immobilized PVP-palladium catalysts were characterized by scanning electron microscopy (SEM), transmission electron microscopy (TEM), Brunauer–Emmett–Teller (BET), infrared spectroscopy (IRS), X-ray powder diffraction (XRD), X-ray photoelectron spectroscopy (XPS), and elemental analysis methods. It was found that the introduction of polymer into the catalyst’s composition promotes the dispersion and uniform distribution of active phase nanoparticles (PdO, Pd⁰) on the surface of zinc oxide. The catalysts were tested in the hydrogenation of complex acetylene alcohol, 3,7,11-trimethyldodecyn-1-ol-3 (C₁₅-yn) under mild conditions (0.1 MPa, 40 °C). For comparison, studies on stereoselective hydrogenation of the short-chain alcohol 2-hexynol-1 were performed. It was shown that modification of the catalyst with polymer improves its catalytic properties. High C₁₅-alkenol selectivity (98%), activity (W = 70 × 10⁻⁶ mol/s), and stability (turnover number (TON) 62,000) were achieved on a Pd-PVP/ZnO catalyst. Varying the active phase made it possible to reduce the metal content without deteriorating the catalytic performance of the catalyst.