Neitzel -- who was benched by Spartans Coach Tom Izzo at the start of the second half for lackadaisical play -- finished with 6-of-12 shooting from beyond the three-point arc and a perfect 10-for-10 from the free-throw line.
Izzo was upset with his team's effort in the first half, even though the Spartans shot 61.1 percent from the floor and took a 31-23 halftime lead. He started the second half with walk-ons Brandon Darnton and DeMarcus Ducre at guard.
Isaiah Dahlman scored 11 points and Marquise Gray had eight points and 11 rebounds for Michigan State (10-2).
Royce Parran scored 20 points and David Holston had 18 for the Cougars (4-9). Kourtney Calvin added 12 points and nine rebounds.