A fundamental difference between antiferromagnets and ferromagnets is the lack of linear coupling to a uniform magnetic field due to the staggered order parameter. Such coupling is possible via the Dzyaloshinskii-Moriya (DM) interaction but at the expense of reduced antiferromagnetic (AFM) susceptibility due to the canting-induced spin anisotropy. We solve this long-standing problem with a top-down approach that utilizes spin-orbit coupling in the presence of a hidden SU(2) symmetry. We demonstrate giant AFM responses to sub-Tesla external fields by exploiting the extremely strong two-dimensional critical fluctuations preserved under a symmetry-invariant exchange anisotropy, which is built into a square-lattice artificially synthesized as a superlattice of SrIrO3 and SrTiO3. The observed field-induced logarithmic increase of the ordering temperature enables highly efficient control of the AFM order. As antiferromagnets promise to afford switching speed and storage security far beyond ferromagnets, our symmetry-invariant approach unleashes the great potential of functional antiferromagnets.