The origin of titanium-rich basaltic magmatism on the Moon remains enigmatic. Ilmenite-bearing cumulates in the lunar mantle are often credited as the source, but their partial melts are not a compositional match and are too dense to enable eruption. Here we use petrological reaction experiments to show that partial melts of ilmenite-bearing cumulates react with olivine and orthopyroxene in the lunar mantle, shifting the melt composition to that of the high-Ti suite. New high-precision Mg isotope data confirm that high-Ti basalts have variable and isotopically light Mg isotope compositions that are inconsistent with equilibrium partial melting. We employ a diffusion model to demonstrate that kinetic isotope fractionation during reactive flow of partial melts derived from ilmenite-bearing cumulates can explain these anomalously light Mg isotope compositions, as well as the isotope composition of other elements such as Fe, Ca and Ti. Although this model does not fully replicate lunar melt–solid interaction, we suggest that titanium-rich magmas erupted on the surface of the Moon can be derived through partial melting of ilmenite-bearing cumulates, but melts undergo extensive modification of their elemental and isotopic composition through reactive flow in the lunar mantle. Reactive flow may therefore be the critical process that decreases melt density and allows high-Ti melts to erupt on the lunar surface.