McDaniel's TD with 14:44 left gave the Fighting Irish (3-1) a 17-10 lead and Notre Dame hung on to record a second consecutive victory.
Tommy Rees struggled behind center, completing just 11-of-31 passes for 135 yards and one touchdown, but Corey Robinson helped out with three grabs for 54 yards.
T.J. Jones scored on a 2-yard scoring pass.
The Spartans (3-1) were led by Connor Cook, who went 16-for-33 for 137 passing yards, one score and an interception.
Jeremy Langford led Michigan State's rushing corps with 69 yards on 14 carries.