The combination of efficient single-photon generation, manipulation, and detection on a single chip poses a major challenge for quantum photonics and all-optical quantum computing. Among a multitude of detection technologies, waveguide-integrated superconducting nanowire single-photon detectors stand out as they promise near-unity detection efficiencies at outstanding timing accuracy and speed. Here, by exploiting the concept of critical coupling, we present the integration of a short nanowire into a two-dimensional double heterostructure photonic crystal cavity to realize an integrated single-photon detector with excellent performance metric. The complete detector characterization reveals on-chip detection efficiencies of almost 70% at telecom wavelengths, recovery times of 480 ps, and vanishingly low dark count rates. Our design paves the way for the implementation of compact on-chip detector arrays and time-multiplexed single-detector schemes.