Single spins in the solid state offer a unique opportunity to store and manipulate quantum information, and to perform quantum-enhanced sensing of local fields and charges. Optical control of these systems using techniques developed in atomic physics has yet to exploit all the advantages of the solid state. Here we demonstrate voltage tunability of the spin energy-levels in a single quantum dot by modifying how spins sense magnetic field. We find that the in-plane g-factor varies discontinuously for electrons, as more holes are loaded onto the dot. In contrast, the in-plane hole g-factor varies continuously. The device can change the sign of the in-plane g-factor of a single hole, at which point an avoided crossing is observed in the two spin eigenstates. This is exactly what is required for universal control of a single spin with a single electrical gate.