We present a carbon nanotube phototransistor using C₆₀ as a sensitizer with responsivity exceeding 10⁷ A/W (10¹⁰ V/W) under visible light. Carbon nanotube/C₆₀ heterojunctions have previously been studied in photovoltaics. However, the responsivity of photovoltaics is limited by its lack of gain, with literature devices having responsivities less than 1 A/W. Our devices display significantly higher responsivity due to their phototransistor structure, with the C₆₀ serving as the sensitizer to a carbon nanotube field-effect transistor. Excitons generated in the C₆₀ diffuse to the heterointerface with the nanotube where they dissociate. Holes transfer to the nanotube and conduct away, leaving electrons bound on the nanotube surface which gate the transistor. The extreme sensitivity of the nanotube to local electric fields then results in a high responsivity. Devices are further improved by using an array of aligned nanotubes, which is significantly better in device current and responsivity compared to random network devices. The resulting devices are sensitive to less than 100 fW of incident light, offering a path forward to single photon detection.