The performance of state-of-the-art perovskite solar cells is currently limited by defect-induced recombination at interfaces between the perovskite and the electron and hole transport layers. These defects, most likely undercoordinated Pb and halide ions, must either be removed or passivated if cell efficiencies are to approach their theoretical limit. In this work, a universal double-side polymer passivation approach is introduced using ultrathin poly(methyl methacrylate) (PMMA) films. Very high-efficiency (≈20.8%) perovskite cells with some of the highest open circuit voltages (1.22 V) reported for the same 1.6 eV bandgap are demonstrated. Photoluminescence imaging and transient spectroscopic measurements confirm a significant reduction in nonradiative recombination in the passivated cells, consistent with the voltage increase. Analysis of the molecular interactions between perovskite and PMMA reveals that the carbonyl (CO) groups on the PMMA are responsible for the excellent passivation via Lewis-base electronic passivation of Pb2+ ions. This work provides new insights and a compelling explanation of how PMMA passivation works, and suggests future directions for developing improved passivation layers.