Resonant coupling between plasmonic nanoantennas and molecular vibrational excitations is employed to amplify the weak overtone transitions that reside in the near-infrared. We explore for the first time the differential extinction of forbidden molecular overtone transitions coupled to the localized surface plasmons. We show a non-trivial interplay between the molecular absorption enhancement and suppression of plasmonic absorption in a coupled system. When the resonance conditions are met at 1.5 µm, two orders of magnitude enhancement of differential extinction as compared to the extinction of the same amount of free probe molecules is achieved. Our results pave a road toward a new class of surface enhanced near-infrared absorption-based sensors.