A detailed study on the ternary Zr-based intermetallic compound Zr2TiAl has been carried out using first-principles electronic structure calculations. From the total energy calculations, we find an antiferromagnetic L11-like (AFM) phase with alternating (1 1 1) spin-up and spin-down layers to be a stable phase among some others with magnetic moment on Ti being 1.22 [Formula: see text]. The calculated magnetic exchange interaction parameters of the Heisenberg Hamiltonian and subsequent Heisenberg Monte Carlo simulations confirm that this phase is the magnetic ground structure with Néel temperature between 30 and 100 K. The phonon dispersion relations further confirm the stability of the magnetic phase while the non-magnetic phase is found to have imaginary phonon modes and the same is also found from the calculated elastic constants. The magnetic moment of Ti is found to decrease under pressure eventually driving the system to the non-magnetic phase at around 46 GPa, where the phonon modes are found to be positive indicating stability of the non-magnetic phase. A continuous change in the band structure under compression leads to the corresponding change of the Fermi surface topology and electronic topological transitions (ETT) in both majority and minority spin cases, which are also evident from the calculated elastic constants and density of state calculations for the material under compression.