We report for the first time the use of a perovskite (CH3NH3PbI3) absorber in combination with ZnO nanorod arrays (NRAs) for solar cell applications. The perovskite material has a higher absorption coeff. than mol. dye sensitizers, gives better solar cell stability, and is therefore more suited as a sensitizer for ZnO NRAs. A solar cell efficiency of 5.0% was achieved under 1000 W m-2 AM 1.5 G illumination for a solar cell with the structure: ZnO NRA/CH3NH3PbI3/spiro-MeOTAD/Ag. Moreover, the solar cell shows a good long-term stability. Using transient photocurrent and photovoltage measurements it was found that the electron transport time and lifetime vary with the ZnO nanorod length, a trend which is similar to that in dye-sensitized solar cells, DSCs, suggesting a similar charge transfer process in ZnO NRA/CH3NH3PbI3 solar cells as in conventional DSCs. Compared to CH3NH3PbI3/TiO2 solar cells, ZnO shows a lower performance due to more recombination losses.