Quasiparticle excitations in UPd2Al3 were studied by means of heat-capacity (C) measurements under rotating magnetic fields using a high-quality single crystal. The field dependence shows C(H)H1/2-like behavior at low temperatures for both two hexagonal crystal axes, i.e., H (c axis) and H (a axis), suggesting the presence of nodal quasiparticle excitations from heavy bands. At low temperatures, the polar-angle (θ) dependence of C exhibits a maximum along H with a twofold symmetric oscillation below 0.5 T, and an unusual shoulder or hump anomaly has been found around 30°-60° from the c axis in C(θ) at intermediate fields (1μ0H2 T). These behaviors in UPd2Al3 purely come from the superconducting nodal quasiparticle excitations, and can be successfully reproduced by theoretical calculations assuming the gap symmetry with a horizontal linear line node. We demonstrate the whole angle-resolved heat-capacity measurements done here as a novel spectroscopic method for nodal gap determination, which can be applied to other exotic superconductors.