Michigan State led by just seven points with 9:45 to play in the opening half and then outscored the Cowboys 24-4 the rest of the way to intermission. McNeese was held to nine points during the first 10 minutes of the second half.
Harris led the Spartans with 20 points and 10 rebounds. He made four shots from 3-point range and was one of six Spartans to reach double figures.
Both Denzel Valentine and Branden Dawson scored 12 points for Michigan State.
Jamaya Burr and Ledrick Eackles were the only members of the Cowboys to reach double figures with 11 points each. McNeese State was limited to 27 percent shooting.