Dynamic control over the full g-tensor in individual InGaAs/GaAs self-assembled quantum dots is achieved by inducing external strain via a piezoelectric actuator. The full g-tensor is obtained by measuring in different geometries with different angles between an externally applied magnetic field and the quantum dot growth axes. A large decrease in the out-of-plane hole g-factor with strain is observed, whereas the other components are found to be less sensitive. To further investigate this, a numerical model based on eight-band k.p-theory is used and an excellent agreement with the experimental results is established, both qualitatively and quantitatively. Furthermore, the calculations reveal the origin of the observed large change in the out-of-plane hole g-factor to be the increase in heavy-hole light-hole splitting under compressive stress.