The cathodoluminescence (CL) spectrum of the synthetic sapphire single crystal has been studied with respect to the different crystallographic planes of the crystal in order to describe the tensorial stress dependence of the band related to oxygen defects. Experiments provide the link between CL spectral shift and stress, which is referred to as the piezo-spectroscopic (PS) relationship. Using the biaxial stress field developed at the tip of cracks generated from the corners of a Vickers indentation, we clearly detected stress dependence for the cumulative band arising from the F+-center transition of optically active oxygen vacancies. The matrix of PS coefficients along different crystallographic axes of single-crystal sapphire could be precisely determined. The shallow nature of the electron probe may enable the characterization of surface stress fields with a spatial resolution that may not be easily available by conventional laser probes. The PS calibration results collected on oxygen-defect bands allow the direct determination of unknown surface residual stress fields stored in sapphire substrates for electronics applications.