By means of a density functional theory approach, we calculated the structural stabilities, electronic structure, elastic constants, and vibrational properties of the compound TiPd₂. The results indicate that the tetragonal MoSi₂-type (C11b) structure is unstable, whereas the orthorhombically distorted MoPt2-type (oI6) structure is the stable ground state phase. Thermodynamical properties such as enthalpies of formation, zero-point energies, and temperature-dependent free energies were calculated. A phase transition from the orthorhombic ground state to the C11b structure was derived for about 1000 K, in reasonable agreement with the most recent experiment. According to our results, the tetragonal-to-orthorhombic structural transition is driven by vibrational entropy.