Inserting an ultrathin low-conductivity interlayer between the absorber and transport layer has emerged as an important strategy for reducing surface recombination in the best perovskite solar cells. However, a challenge with this approach is a trade-off between the open-circuit voltage (Voc) and the fill factor (FF). Here, we overcame this challenge by introducing a thick (about 100 nanometers) insulator layer with random nanoscale openings. We performed drift-diffusion simulations for cells with this porous insulator contact (PIC) and realized it using a solution process by controlling the growth mode of alumina nanoplates. Leveraging a PIC with an approximately 25% reduced contact area, we achieved an efficiency of up to 25.5% (certified steady-state efficiency 24.7%) in p-i-n devices. The product of Voc × FF was 87.9% of the Shockley-Queisser limit. The surface recombination velocity at the p-type contact was reduced from 64.2 to 9.2 centimeters per second. The bulk recombination lifetime was increased from 1.2 to 6.0 microseconds because of improvements in the perovskite crystallinity. The improved wettability of the perovskite precursor solution allowed us to demonstrate a 23.3% efficient 1-square-centimeter p-i-n cell. We demonstrate here its broad applicability for different p-type contacts and perovskite compositions.