Using laser-induced fluorescence-dip Stark spectroscopy, we performed time-resolved, direct measurements of electric-field strengths during the breakdown phase of a low-pressure, pulsed discharge in xenon. With this experimental technique we could for the first time quantitatively measure the time evolution of the driving force of the plasma breakdown process: the electric field. Moving ionization fronts were measured with submicrosecond resolution. These ionization fronts were sustained by a spatially narrow, rapidly moving region of strong electric field.