Through the theoretical study of electron spin lifetime in the two-dimensional electron gas (2DEG) confined near the surface of doped Si, we highlight a dominant spin-relaxation mechanism induced by the impurity central-cell potential near an interface via intervalley electron scattering. At low temperatures and with modest doping, this Yafet spin-flip mechanism can become more important than the D yakonov-Perel spin relaxation arising from the structural Rashba or Dresselhaus spin-orbitcoupling field. As the leading-order impurity-induced spin flip happens only between two nonopposing valleys in Si, 2DEG systems in Si MOSFETs or SiGe heterostructures are a natural platform to test and utilize this spin-relaxation mechanism due to the valley splitting near the interface and the tunability by electrical gating or applied stress. Our proposed alternative spin-relaxation mechanism may explain part of the spin-relaxation contribution to Si-based 2DEG systems, and it should have spintronic applications in Si-based devices.