Michigan State (18-8, 5-6 Big Ten) went on a 7-0 scoring spurt midway through the second half to take a 36-29 lead, highlighted by a Morgan 3-point play on a basket and a foul shot.
The Wolverines (17-9, 5-6) crept back within 2 points twice. But key buckets by Morgan and Neitzel held off the comeback.
A Neitzel 3-pointer gave the Spartans a 47-36 lead with about 4 minutes remaining.
Dion Harris led Michigan with 13 points.
Michigan hasn't won in East Lansing since 1997. The Spartans have won 14 of the last 16 meetings overall.
Both teams have struggled in the past few weeks, dropping below .500 in the Big Ten and putting their hopes of making the NCAA tournament in jeopardy.
Both the Spartans and Wolverines need more wins in their quest to make the tournament. Both teams have five games remaining in the regular season, including a Feb. 27 rematch in Ann Arbor, followed by the Big Ten tournament.
Michigan State has qualified for the NCAA tournament nine consecutive seasons, the longest current streak in the Big Ten.
Michigan hasn't made the NCAA field since 1998.
Both teams played aggressive, solid defense in a low-scoring first half. Michigan led by as many as 5 points in the first half, but the Spartans finished the half with a 24-23 lead on a Neitzel 3-pointer.
Michigan State hasn't lost five in a row since the 1996-97 season.