Steam methane reforming (SMR) is by far the dominant approach of hydrogen production, but its feasibility for producing low-carbon-footprint H2 has been constrained by high reaction temperatures (>800 degrees C), complexity of processes, and high energy penalties associated with H2 and CO2 separation. To address such key challenges, we propose a new principle of multi-product sequential separation and a new method of sequential separation-driven SMR for the first time. Target product species H2 and CO2 are sequentially separated, so that their partial pressures are maintained close to their maxima at thermodynamic equilibrium to effectively drive methane conversion to full completion theoretically. The new principle enables a remarkable decrease in the SMR temperature and a dramatic reduction in energy penalties of separation in theory and practice. The effectiveness of the new principle and method is demonstrated by a proof-of-concept reactor with a Pd-Ag membrane and alternating nickel catalyst/hydrotalcite sorbent combinations. High-purity H2 and CO2 are directly obtained with >99% conversion of methane and >99% yield and selectivity of H2 and CO2 under mild conditions of 400 degrees C and 1 bar. Fast and stable production of H2 and CO2 is demonstrated over 6000 cycles. The highly compact reactor and mild operating conditions further enable integration with a parabolic trough solar collector, by which mid-temperature solar thermochemical H2 production and CO2 capture are achieved. The solar-to-H2 efficiency is 3.4% with direct solar illumination. The efficiency can be enhanced to 46.5% or above with solar thermal energy storage and advances in mid-/low-temperature SMR catalysts and CO2 sorbents, and can be further enhanced to beyond 60% with low-energy-penalty separation technologies.