In this study, as a product from the efficient Achmatowicz rearrangement and mild subsequent hydrogenation–reduction reactions of biorenewable C5 alcohols derived from lignocellulose, pentane-1,2,5-triol was successfully used after oxypropylation in the preparation of rigid polyurethane foams—one of the most important classes of polymeric materials. Despite the broad range of applications, the production of polyurethanes is still highly dependent on petrochemical materials considering the need of renewable raw materials and new process technologies for the production of polyol or isocyanate components as a key point for the sustainable development of polyurethane foams. The synthesized oxypropylated pentane-1,2,5-triol was analyzed using proton NMR spectroscopy, hydroxyl number, and viscosity, whereas the newly obtained foams incorporated with up to 30% biorenewable polyol were characterized using compressive stress, thermogravimetry, dynamic mechanical analysis, and scanning electron microscopy. The modified rigid polyurethanes showed better compressive strength (>400.0 kPa), a comparable thermal degradation range at 325–450 °C, and similar morphological properties to those of commercial polyurethane formulations.