When you apply at Stanford for the Engineer's Degree if you get accepted you will be in the M.S. program. The Engineer's Degree comes after the completion of the M.S. with an additional 45 units of coursework which includes a thesis. You apply during your time doing the M.S. program and I think you have to be recommended or have a certain GPA in the M.S. program to move on to the Engineer's Degree.
I'd say if you have a GPA over a 3.5 and GRE score with a quantitative score above 770ish you have a decent chance of being accepted to M.S. at Stanford of course it depends on schoolwork, LOR, and essays.