We present a homogeneous set of accurate atmospheric parameters for a sample of eleven very metal-poor (-3.32 <= [Fe/H] <=-2.61) stars in the Sextans dwarf spheroidal galaxy (dSph) and the non-local thermodynamic equilibrium (NLTE) abundances of, at least, seven chemical elements based on high-resolution UVES/VLT and HDS/Subaru spectra. For each star, its effective temperature and surface gravity were derived from the spectral energy distribution and the known distance, and the Fe abundance was obtained as the average from lines of Fe i and Fe ii. Based on abundances of Mg, Ca, and Ti, we show that all the investigated stars reveal alpha-enhancements of 0.4 dex to 0.2 dex, and there is a hint of a decline in alpha/Fe for [Fe/H] >-2.8. The Sextans stars are deficient in Ba. The new result is an extremely tight relation between Ba and Mg, suggesting their common origin in massive stars and Ba synthesis in the r-process events on the time-scales of standard supernovae. The exception is a C-enhanced star S 15-19 which is strongly enhanced in Ba. This star is unlikely to be a CEMP-s star because of low abundances of Sr and Y ([Y/Fe] <-1) that are produced in the s-process as efficiently as Ba and a non-detection of variation in the radial velocity. No distinctions from the Milky Way halo and the Sculptor and Ursa Minor dSphs were found in a history of early enrichment in Na and Ni, namely, the Sextans stars are deficient in Na and have close-to-solar Ni/Fe.