In a semiconductor quantum dot, the Pi(x) and Pi(y) transitions to the polarization eigenstates, vertical bar x > and vertical bar y >, naturally form a three-level V-type system. Using low-temperature polarized photoluminescence spectroscopy, we have investigated the exciton dynamics arising under strong laser excitation. We also explicitly solved the density matrix equations for comparison with the experimental data. The polarization of the exciting field controls the coupling between the otherwise orthogonal states. In particular, when the system is initialized into vertical bar y >, a polarization-tailored pulse can swap the population into vertical bar x >, and vice versa, effectively operating on the exciton spin.