The spectral-, position- and tracking-response of Timepix to energetic electrons has been tested and characterized with well-defined low-intensity parallel beams of monoenergetic electrons in the 7 e21 MeV range. The per-pixel energy sensitivity of Timepix serves as a position-sensitive dE/dx detector to determine the energy loss over along the particle track. The sampling path pitch can be set to 55 mm (pixel-size) and arbitrary values between 300 mm (sensor thickness) and nearly 2 mm. Timepix can register and visualize not only the position and trajectories but also the direction of trajectories and the rate of directional scattering of single fast electrons across the semiconductor sensor. The technique serves to measure the spatial distribution of a parallel beam, the beam size spread, transversal beam flux homogeneity and lateral straggling at the pixel-size scale. The mean scattering path along the beam axis and the mean path for lateral beam straggling in silicon can be determined. Measured energy loss distributions were compared with model and previous data as well as with dedicated Monte Carlo MCNPX simulations performed for this work. Tracking distributions were also simulated.