Accurate, in-field-compatible, sensing based on near infrared spectroscopy (NIRS) requires development of instrumentation with low noise and long-term stability. Here, we present a fully fiber-optic spectroscopy setup using a supercontinuum source in the long-pulse regime (2 ns) and a balanced detector scheme to demonstrate high-accuracy NIRS-based sensing. The noise sources of the system are studied theoretically and experimentally. The relative intensity noise was reduced from typical values up to 6% to less than 0.1% by deploying a balanced detector and averaging. At well-balanced wavelengths, the system without transmission cells achieved a signal to noise ratio (SNR) above 70 dB, approaching the shot noise limit. With transmission cells and long-term measurements, the overall SNR was 55 dB. Glucose in physiological concentrations was measured as a model system, yielding a root mean square error of 4.8 mM, approaching the needed accuracy for physiological glucose monitoring.