The PAMELA space experiment, in orbit since 2006, has measured cosmic rays through the most recent A < 0 solar minimum activity period. During this entire time, galactic electrons and protons have been detected down to 70 MV and 400 MV, respectively, and their differential intensity variation in time has been monitored with unprecedented accuracy. These observations are used to show how differently electrons and protons responded to the quiet modulation conditions that prevailed from 2006 to 2009. It is well known that particle drifts, as one of four major mechanisms for the solar modulation of cosmic rays, cause charge-sign dependent solar modulation. Solar minimum activity periods provide optimal conditions to study these drift effects. The observed behaviour is compared to the solutions of a three-dimensional model for cosmic rays in the heliosphere, including drifts. The numerical results confirm that the difference in the evolution of electron and proton spectra during the last prolonged solar minimum is attributed to a large extent to particle drifts. We therefore present new evidence of charge-sign dependent solar modulation, with perspective on its peculiarities for the observed period from 2006 to 2009.