We demonstrate that the intense electric field of a subpicosecond single-cycle terahertz pulse can control and manipulate the temporal, spectral, and spatial phase of a copropagating ultrashort laser pulse through the Pockels effect in an electro-optic crystal. In the temporal and spectral domains, the single-cycle THz pulse can impart either a positive or a negative quadratic phase modulation to the probe pulse, leading to a spectral shift, broadening, or pulse expansion or compression. While acting in the spatial domain, the THz-induced phase modulation induces a lenslike effect, providing focusing or defocusing of the copropagating probe beam. The experimental results are in good agreement with simulations. Our study gives a comprehensive picture of the nonlinear spatiotemporal dynamics in the high-field regime driven by the intense single-cycle THz pulse.