The advent of quantum optics and quantum information processing goes hand in hand with the search for adequate active and passive components operating on the single-photon level at telecommunication wavelengths. Among a variety of approaches, a hybrid arrangement of integrated single-photon sources, reconfigurable photonic circuitry, and detectors on a single chip is particularly promising with respect to complexity, compactness, reproducibility, stability, and ease of fabrication. While a multitude of detection technologies are currently investigated, waveguide-integrated superconducting nanowire single-photon detectors stand out due to their 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. Compared to photonic crystal nanobeam cavities, our overhauled design approach reduces outscattering losses and can readily be combined with single-photon emitters integrated into on-chip cavities. Our silicon photonics approach paves the way for the implementation of compact on-chip detector arrays and time-multiplexed single-detector schemes.