We report a strong selective enhancement of electronic intersubband excitations of a modulation-doped GaAs-Al0.2Ga0.8As quantum well placed inside an AlAs-Al0.4Ga0.6As planar lambda microcavity. By using specific angles for the incident and scattered light, both the exciting laser and the scattered photons can be tuned into resonance with the cavity mode. Since the width of the high-quality cavity mode is smaller than the widths of the electronic excitations, we can, in the double-resonance case, selectively enhance parts of the excitations by about 3 orders of magnitude compared to the single-resonance condition. This offers the possibility to selectively study weak electronic excitations in low-dimensional electron systems.