The rate of neutrino-electron elastic scattering interactions from 862 keV Be solar neutrinos in Borexino is determined to be 46.0+/-1.5(stat)+1:5/-1:6(syst) counts/(day •100 ton). This corresponds to a ve-equivalent Be solar neutrino flux of (3.10+/-0.15) ×109 cm-2s-1 and, under the assumption of ve transition to other active neutrino flavors, yields an electron neutrino survival probability of 0.51+/-0.07 at 862 keV. The no flavor change hypothesis is ruled out at 5.0σ. A global solar neutrino analysis with free fluxes determines ϕpp=6.06+0:02 /-0:06×1010 cm-2s-1 and ϕCNO<1.3×109 cm-2s-1 (95% C.L.). These results significantly improve the precision with which the MSW-LMA neutrino oscillation model is experimentally tested at low energy.