We report a type of structural phase transitions in dielectric materials: the triggered incommensurate (IC) transition. We demonstrate evidence for such a transition in the perovskite antiferroelectric PbHfO3 by means of single-crystal x-ray diffraction, diffuse, and inelastic-scattering experiments, which we interpret using the Landau theory of phase transitions. This transition is not driven by an IC soft mode, as is the case for the majority of IC dielectrics, but by the soft mode associated with a different, coexisting order parameter related to antiferrodistortive (AFD) tilts of the oxygen octahedra. When cooling from the high-temperature cubic phase these two order parameters are established simultaneously and discontinuously at T-IC approximate to 468 K. Two lattice instabilities are present in the cubic phase: AFD instability with critical temperature T-0 approximate to 441 K and ferroelectric instability with T-0 approximate to 408 K. The IC instability is absent. The analysis of the transition mechanism within the Landau theory of coupled order parameters indicates that the transition is of triggered character, conditioned upon the attractive biquadratic coupling between the IC modulation and the AFD octahedral tilts, and is driven by the AFD soft mode.