One of the main neutron sources for the astrophysical s-process is the 13C(α,n)16O. This reaction takes place in thermally pulsing asymptotic giant branch (TP-AGB) stars in a stellar environmental with temperature of about 90 MK. To model the nucleosynthesis process connected with the reaction, it is important the cross section reaction evaluation inside the so called Gamow peak, in the energy window 150-240 keV. In this work the results of the first 13C(α,n)16O direct measurement performed by the LUNA collaboration in the underground laboratory of LNGS are presented.The measurement covers the energy range 230-300 keV, being the first direct measurement to reach the s-process Gamow window. Lower uncertainties with respect to previous measurements in literature are provided and this allows to reduce overall uncertainties on reaction rates calculation. Selected stellar models have been computed to estimate the impact of our revised reaction rate. Using the lower reaction rate at -2σ, for stars of nearly solar composition, we find sizeable variations for some isotopes, whose production is influenced by the activation of close-by branching points that are sensitive to the neutron density, in particular 60Fe, 205Pb and and 152Gd.