Integrated spectrometers hold great promise for in-situ, in vitro, and even in vivo near-infrared (NIR) sensing applications. However, practical NIR applications require fine resolution, high accuracy, and mostly importantly, ultra-wide observation window that spans multiple overtone regions, for capturing spectral fingerprints. In this paper, we present an integrated reconstructive spectrometer utilizing dispersion-engineered ring resonators, achieving an over 520 nm operational bandwidth together with a superior resolution of less than 8 pm. This translates into an over 65,000 bandwidth-to-resolution ratio that represents a significant record breakthrough for miniaturized spectrometers. Moreover, we showcase a packaged spectrometer chip with auxiliary electronics, creating a fully functional NIR spectroscopic sensor. Various bandwidth-demanding NIR sensing applications are examined, including the classification of different types of solid substances and the concentration test of aqueous and organic solutions, all achieving approximately 100% accuracy. Specifically, we test the sensor's detection limit using glucose solutions and successfully identify concentrations as low as 0.1% (i.e. 100 mg/dL), which matches that of the commercial benchtop counterparts and sets up a new benchmark for miniaturized spectroscopic sensors.