Nanostructured metals have utilized the strong spatial confinement of surface plasmon polaritons to harness enormous energy densities on their surfaces, and have demonstrated vast potential for the future of nano-optical systems and devices. While the spectral location of the plasmonic resonance can be tailored with relative ease, the control over the spectral linewidth associated with loss represents a more daunting task. In general, plasmonic resonances typically exhibit a spectral linewidth of ~50 nm, limited largely by the combined damping and radiative loss in nanometallic structures. Here, we present one of the sharpest resonance features demonstrated by any plasmonic system reported to date by introducing dark plasmonic modes in diatomic gratings. Each duty cycle of the diatomic grating consists of two nonequivalent metallic stripes, and the asymmetric design leads to the excitation of a dark plasmonic mode under normal incidence. The dark plasmonic mode in our structure, occurring at a prescribed wavelength of ~840 nm, features an ultra-narrow spectral linewidth of about 5 nm, which represents a small fraction of the value commonly seen in typical plasmonic resonances. We leverage the dark plasmonic mode in the metallic nanostructure and demonstrate a resonance enhanced plasmoelectric effect, where the photon-induced electric potential generated in the grating is shown to follow the resonance behavior in the spectral domain. The light concentrating ability of dark plasmonic modes in conjunction with the ultra-sharp resonance feature at a relatively low loss offers a novel route to enhanced light-matter interactions with high spectral sensitivity for diverse applications.