Miniaturized computational spectrometers, which can obtain incident spectra using a combination of device spectral response and reconstruction algorithms, are essential for on-chip and implantable applications. Highly sensitive spectral measurement using a single detector allows the footprints of such spectrometers to be scaled down while achieving spectral resolution approaching that of benchtop systems. We report a high-performance computational spectrometer based on a single van der Waals junction with an electrically tunable transport-mediated spectral response. We achieve high peak wavelength accuracy (~0.36 nanometers), high spectral resolution (~3 nanometers), broad operation bandwidth (from ~405 to 845 nanometers), and proof-of-concept spectral imaging. Our approach provides a route toward ultraminiaturization and offers unprecedented performance in accuracy, resolution, and operation bandwidth for single-detector computational spectrometers.