We report the observation of a spin-flip process in a quantum dot whereby a dark exciton with total angular momentum L = 2 becomes a bright exciton with L = 1. The spin-flip process is revealed in the decay dynamics following nongeminate excitation. We are able to control the spin-flip rate by more than an order of magnitude simply with a dc voltage. The spin-flip mechanism involves a spin exchange with the Fermi sea in the back contact of our device and corresponds to the high temperature Kondo regime. We use the Anderson Hamiltonian to calculate a spin-flip rate, and we find excellent agreement with the experimental results.