  Creating and manipulating spin polarization in low-dimensional electron
systems (such as two-dimensional electron gases) is fundamentally essential for
spintronic applications, which is yet a challenge to date. In this work, we
establish the metamagnetic phase diagram of 4$f$ antiferromagnetic TbScO$_3$
and reveal its giant magnetic response to sub-tesla magnetic field, which has
not been reported thus far. Utilizing this giant magnetic response, we
demonstrate that the spin polarization of two-dimensional electron gas in
SrTiO$_3$/LaTiO$_3$/TbScO$_3$ heterostructure can be manipulated successfully
in aid of interfacial 3\textit{d}-4\textit{f} exchange interaction. Remarkably,
the hysteretic magnetoresistances of two-dimensional electron gas at the
SrTiO$_3$/LaTiO$_3$ interface are entirely determined by the metamagnetic phase
transitions of the underlying TbScO$_3$ substrate. Our results pave a novel
route to engineer the spin polarization of low-dimensional electron systems in
4$f$ antiferromagnet-based heterostructures.
