  Semiconductor holes with strong spin-orbit coupling allow all-electrical spin
control, with broad applications ranging from spintronics to quantum
computation. Using a two-dimensional hole system in a GaAs quantum well, we
demonstrate a new mechanism of electrically controlling the Zeeman splitting,
which is achieved through altering the hole wave vector $k$. We find a
threefold enhancement of the in-plane $g-$factor $g_{\parallel}(k)$. We
introduce a new method for quantifying the Zeeman splitting from
magnetoresistance measurements, since the conventional tilted field approach
fails for two-dimensional systems with strong spin-orbit coupling. Finally, we
show that the Rashba spin-orbit interaction suppresses the in-plane Zeeman
interaction at low magnetic fields. The ability to control the Zeeman splitting
with electric fields opens up new possibilities for future quantum spin-based
devices, manipulating non-Abelian geometric phases, and realising Majorana
systems in $p-$type superconductor systems.
