The lunar basalt samples returned by the Chang’e-5 mission erupted about 2.0 billion years ago during the late period of the Moon’s secular cooling. The conditions of mantle melting in the source region and the migration of magma through the thick lithosphere that led to this relatively late lunar volcanism remain open questions. Here we combine quantitative textural analyses of Chang’e-5 basaltic clasts, diffusion chronometry, clinopyroxene geothermobarometers and crystallization simulations to establish a holistic picture of the dynamic magmatic–thermal evolution of these young lunar basalts. We find that the Chang’e-5 basalts originated from an olivine-bearing pyroxenite mantle source (10–13?kbar or 250?±?50?km; 1,350?±?50?°C), similar to Apollo 12 low-Ti basalts. We propose these magmas then ascended through the plumbing system and accumulated mainly at the top of the lithospheric mantle (~2–5?kbar or 40–100?km, 1,150?±?50?°C), where they stalled at least several hundred days and evolved via high-degree fractional crystallization. Finally, the remaining evolved melts erupted rapidly onto the surface over several days. Our magmatic–thermal evolution model indicates abundant low-solidus pyroxenites in the mantle source with a slightly enhanced inventory of radioactive elements can explain the prolonged, but declining, lunar volcanism up to about 2 billion years ago and beyond.