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 spinorbit coupling field. As the leading-order impurity-induced spin flip happens only between two non-opposite 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 new spin relaxation mechanism may explain a part of the spin relaxation contribution to Si-based 2DEG systems, and should have spintronic applications in Si-based devices.