We theoretically investigate the spin-resolved local density of states (SR-LDOS) of a spin-polarized twodimensional electron gas in the presence of a Kondo adatom and a scanning tunneling microscopy probe. Using Green's function formalism and the atomic approach in the limit of infinite Coulomb correlation, an analytical SR-LDOS expression in the low-temperature regime of the system is found. This formal result is given in terms of phase shifts originated by the adatom scattering and Fano interference. The SR-LDOS is investigated as a function of the probe position and different Fano factors. Our findings provide an alternative way to spin split the Kondo resonance without the use of huge magnetic fields, typically necessary in adatom systems characterized by large Kondo temperatures. We observe a non-Zeeman spin splitting of the Kondo resonance in the total LDOS, with one spin component pinned around the host Fermi level. Interestingly, this result is in accordance to recent experimental data [Phys. Rev. B 82, 020406R (2010)].