Eukaryotic cells chemosense concentration gradients of extracellular ligands using membrane-bound receptors that polarize their activity. Receptors from several chemosensing families are preferentially degraded after activation and undergo significant lateral diffusion, both of which may blunt their polarization. To explore the combined role of these two seemingly detrimental phenomena on active receptor polarization, we use a reaction/diffusion model. The model elucidates a counterintuitive principle that governs receptor polarization under external gradients: Localized Activity and Global Sensitization (LAGS). In LAGS, receptor activity is localized through receptor degradation or ligand unbinding. In contrast, uniform sensitivity to ligands is maintained over the plasma membrane through lateral receptor diffusion. Surprisingly, increasing preferential degradation of active receptors and increasing lateral diffusion of all receptors both sharpen active receptor polarization. Additionally, when combined with receptor oligomerization, an increase in preferential degradation allows cells to sense relative ligand gradients over a larger range of background ligand concentrations. An analytical model identifies parameter regimes that dictate which processes dominate receptor polarization. A survey of kinetic parameters suggests that receptor polarization in many mammalian pathways can be modeled using LAGS.