We report for the first time on a hole conductor-free mesoscopic methylammonium lead iodide (CH₃NH₃PbI₃) perovskite/TiO₂ heterojunction solar cell, produced by deposition of perovskite nanoparticles from a solution of CH₃NH₃I and PbI₂ in γ-butyrolactone on a 400 nm thick film of TiO₂ (anatase) nanosheets exposing (001) facets. A gold film was evaporated on top of the CH₃NH₃PbI₃ as a back contact. Importantly, the CH₃NH₃PbI₃ nanoparticles assume here simultaneously the roles of both light harvester and hole conductor, rendering superfluous the use of an additional hole transporting material. The simple mesoscopic CH₃NH₃PbI₃/TiO₂ heterojunction solar cell shows impressive photovoltaic performance, with short-circuit photocurrent J_sc= 16.1 mA/cm², open-circuit photovoltage V_oc = 0.631 V, and a fill factor FF = 0.57, corresponding to a light to electric power conversion efficiency (PCE) of 5.5% under standard AM 1.5 solar light of 1000 W/m² intensity. At a lower light intensity of 100W/m², a PCE of 7.3% was measured. The advent of such simple solution-processed mesoscopic heterojunction solar cells paves the way to realize low-cost, high-efficiency solar cells.