We have investigated the structural phase transitions of the transition metal oxide perovskites SrTiO3, LaAlO3, and LaTiO3 using the screened hybrid density functional of Heyd, Scuseria, and Ernzerhof (HSE06). We show that HSE06-computed lattice parameters, octahedral tilts, and rotations, as well as electronic properties, are significantly improved over semilocal functionals. We predict the crystal-field splitting (ΔCF) resulting from the structural phase transition in SrTiO3 and LaAlO3 to be 3 meV and 10 meV, respectively, in excellent agreement with experimental results. HSE06 identifies correctly LaTiO3 in the magnetic states as a Mott insulator. Also, it predicts that the GdFeO3-type distortion in nonmagnetic LaTiO3 will induce a large ΔCF of 410 meV. This large crystal-field splitting associated with the large magnetic moment found in the G-type antiferromagnetic state suggests that LaTiO3 has an induced orbital order, which is confirmed by the visualization of the highest occupied orbitals. These results strongly indicate that HSE06 is capable of efficiently and accurately modeling perovskite oxides and promises to efficiently capture the physics at their heterointerfaces.