Using the near-infrared spectral stellar library of Cenarro et al., the behaviour of the MgI line at 8807 Å and nearby TiO bands is 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 two new indices exhibit interesting properties. In particular, MgI is 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 function 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, an [Mg/Fe] underabundance of ~ -0.04 is derived for the Galactic open cluster M67.