Enhanced absorption of especially long wavelength light is needed to enable the full potential of semiconductor nanowire (NW) arrays for optoelectronic applications. We show both experimentally and theoretically that a transparent dielectric shell (Al2O3 coating) can drastically improve the absorption of light in InAs NW arrays. With an appropriate thickness of the Al2O3 shell, we achieve four times stronger absorption in the NWs compared to uncoated NWs and twice as good absorption as when the dielectric completely fills the space between the NWs. We provide detailed theoretical analysis from a combination of full electrodynamic modeling and intuitive electrostatic approximations. This reveals how the incident light penetrates better into the absorbing NW core with increasing thickness of the dielectric shell until a resonant shell thickness is reached. We provide a simple description of how to reach this strongly absorbing resonance condition, making our results easy to apply for a broad wavelength range and a multifold of semiconductor and dielectric coating material combinations.