Neitzel had 14 points, including three 3s, in the second half as the Spartans (7-2) pulled away. It was his fourth 20-point effort in the last five games.
Morgan was 8-for-10 at the foul line and grabbed seven rebounds in a game with sensational long-range shooting and several long scoring runs.
Travis Walton had two career-highs with 15 points and nine assists. He hit all three of his 3-point tries.
The bench also delivered. Marquise Gray added 11 points, including three rim-rattling dunks, while Drew Naymich grabbed 10 rebounds.
Michigan State sandwiched a 14-2 Bradley surge with 15-0 and 10-0 spurts to take a 29-21 halftime lead. The Spartans blew it open after the break with nine quick points, then had another 16-0 run to go up by 35 with nine minutes left.