Spatiotemporal optical vortices (STOVs) are structured light featuring a phase singularity in the spatiotemporal domain, exhibiting unique topology that couples spatial and temporal dimensions. To date, amplification of STOVs remains unexplored, and their wavelength tunability is limited by available light sources. In this work, we present the theoretical analysis and experimental demonstration of optical parametric amplification (OPA) of STOVs. The pulse energy of the STOV signal is enhanced by a factor of 60, while its spatiotemporal structure is robustly preserved. The generated idler inherits the phase-conjugated STOV topology with the opposite topological charge, governed by simultaneous conservation of energy, linear momentum, and spatiotemporal orbital angular momentum. The intrinsic wavelength-conversion capability of OPA further provides a route towards spectrally tunable STOV generation, spanning from visible to near-infrared wavelength regimes. This work paves the way toward further development of multi-stage amplification architectures, facilitating applications of wavelength-tunable spatiotemporally structured light at ultrahigh intensities.