Green, coming off a triple-double performance in the Spartans' previous game, also dished off six assists as Michigan State (29-7) advanced to the Sweet 16 for the third time in four years.
Keith Appling got hot in the second half, scoring 15 of his 19 points in the after the break in the Spartans' win.
Derrick Nix and Brandon Wood contributed 10 points each for MSU.
Saint Louis (26-8), meanwhile, came up short in its bid for a first-ever Sweet 16 appearance.
Kwamain Mitchell supplied 13 points and Brian Conklin added 11 for the Billikens.