An excitation function of one- and two-neutron transfer channels for the ^{60}Ni+^{116}Sn system has been measured with the magnetic spectrometer PRISMA in a wide energy range, from the Coulomb barrier to far below it. The experimental transfer probabilities are well reproduced, for the first time with heavy ions, in absolute values and in slope by microscopic calculations which incorporate nucleon-nucleon pairing correlations.