Using the near-infrared spectral stellar library of Cenarro et al. (2001a,b), the behaviours of the Mg I line at 8807 A and nearby TiO bands are analyzed in terms of the effective temperature, surface gravity, and metallicity of the library stars. New spectroscopic indices for both spectral features -namely MgI and sTiO- are defined, and their sensitivities to different signal-to-noise ratios, spectral resolutions, flux calibrations, and sky emission line residuals are characterized. The new two indices exhibit interesting properties. In particular, MgI reveals as a good indicator of the Mg abundance, whereas sTiO is a powerful dwarf-to-giant discriminator for cold spectral types. Empirical fitting polynomials that reproduce the strength of the new indices as a function of the stellar atmospheric parameters are computed, and a FORTRAN routine with the fitting functions predictions is made available. A thorough study of several error sources, non-solar [Mg/Fe] ratios, and their influence on the fitting function residuals is also presented. From this analysis, a [Mg/Fe] underabundance of ~ -0.04 is derived for the Galactic open cluster M67.