Summers had six rebounds to go with Green's 18 points and 12 boards for the Spartans (2-0).
Devon Green finished with 15 points and six rebounds.
Bruce Ellington scored 22 and Brian Richardson added 11 to lead South Carolina (1-1).
Michigan State cruised to a 42-25 lead at halftime but the Gamecocks scored 48 in the second half to the Spartans' 40. Michigan State was able to keep the visitors at arm's length, however, and maintained at least an 8-point advantage the rest of the way.