Near-field coupling between a silicon quantum dot (Si-QD) monolayer and a plasmonic substrate fabricated by nano-imprint lithography and having broad multiple resonances in the near-infrared (NIR) window of biological substances was studied by precisely controlling the QDs-substrate distance. A strong enhancement of the NIR photoluminescence (PL) of Si-QDs was observed. Detailed analyses of the PL and PL excitation spectra, the PL decay dynamics, and the reflectance spectra revealed that both the excitation cross-sections and the emission rates are enhanced by the surface plasmon resonances, thanks to the broad multiple resonances of the plasmonic substrate, and that the relative contribution of the two enhancement processes depends strongly on the excitation wavelength. Under excitation by short wavelength photons (405 nm), where enhancement of the excitation cross-section is not expected, the maximum enhancement was obtained when the QDs-substrate distance was around 30 nm. On the other hand, under long wavelength excitation (641 nm), where strong excitation cross-section enhancement is expected, the largest enhancement was obtained when the distance was minimum (around 1 nm). The achievement of efficient excitation of NIR luminescence of Si-QDs by long wavelength photons paves the way for the development of Si-QD-based fluorescence bio-sensing devices with a high bound-to-free ratio.