Experimental results of inclusive hard-process cross sections in heavy-ion collisions conventionally lean on a normalization computed from Glauber models where the inelastic nucleon-nucleon cross section σ_{nn}^{inel}-a crucial input parameter-is simply taken from proton-proton measurements. In this Letter, using the computed electroweak boson production cross sections in lead-lead collisions as a benchmark, we determine σ_{nn}^{inel} from the recent ATLAS data. We find a significantly suppressed σ_{nn}^{inel} relative to what is usually assumed, show the consequences for the centrality dependence of the cross sections, and address the phenomenon in an eikonal minijet model with nuclear shadowing.