The dc Stark shift of the D1 lines of rubidium and potassium are observed using a pair of cavitystabilized diode lasers locked to resonance signals. The heterodyne signal from the two lasers and the optical measurements of the electrode spacing yield high-precision results. The observed scalar shifts are found to be 61.153(8) kHz (kV/cm) ' for rubidium and 39.400(5) kHz (kV/cm) for potassium.These results represent more than three orders of magnitude improvement in our knowledge of these Stark shifts.PACS number(s): 32.60.+i, 35.10.Di, 35.80.+s