We predict a new electron pair tunneling (PT) resonance in nonlinear transport through quantum dots with positive charging energies exceeding the broadening due to thermal and quantum fluctuations. The PT resonance shows up in the single-electron transport (SET) regime as a peak in the derivative of the nonlinear conductance, d(2)I/dV(2), when the electrochemical potential of one electrode matches the average of two subsequent charge addition energies. For a single level quantum dot (Anderson model) we find the analytic peak shape and the dependence on temperature, magnetic field, and junction asymmetry and compare with the inelastic cotunneling peak which is of the same order of magnitude. In experimental transport spectroscopy the PT resonance may be mistaken for a weak SET resonance judging only by the voltage dependence of its position. Our results provide essential clues to avoid such erroneous interpretation.