Although the existence of the twist-bend (NTB) and splay-bend (NSB) nematic phases was predicted long ago, only the former has as yet been observed experimentally, whereas the latter remains elusive. This is especially disappointing because the NSB nematic is promising for applications in electro-optic devices. By applying an electric field to a planar cell filled with the compound CB7CB, we have found an NTB-NSB phase transition using birefringence measurements. This field-induced transition to the biaxial NSB occurred, although the field was applied along the symmetry axis of the macroscopically uniaxial NTB. Therefore, this transition is a counterintuitive example of breaking of the macroscopic uniaxial symmetry. We show by theoretical modeling that the transition cannot be explained without considering explicitly the biaxiality of both phases at the microscopic scale. This strongly suggests that molecular biaxiality should be a key factor favoring the stability of the NSB phase.