Imperfections in organometal halide perovskite films such as grain boundaries (GBs), defects, and traps detrimentally cause significant nonradiative recombination energy loss and decreased power conversion efficiency (PCE) in solar cells. Here, a simple layer-by-layer fabrication process based on air exposure followed by thermal annealing is reported to grow perovskite films with large, single-crystal grains and vertically oriented GBs. The hole-transport medium Spiro-OMeTAD is then infiltrated into the GBs to form vertically aligned bulk heterojunctions. Due to the space-charge regions in the vicinity of GBs, the nonradiative recombination in GBs is significantly suppressed. The GBs become active carrier collection channels. Thus, the internal quantum efficiencies of the devices approach 100% in the visible spectrum range. The optimized cells yield an average PCE of 16.3 +/- 0.9%, comparable to the best solution-processed perovskite devices, establishing them as important alternatives to growing ideal single crystal thin films in the pursuit toward theoretical maximum PCE with industrially realistic processing techniques.