The Spartans overcame a 10-point halftime deficit by holding the Illini scoreless for the first 4:38 of the second period and eventually fought off the upset bid.
Appling made 7-of-12 from the field and he hit a clutch shot with 48 seconds left that gave the Spartans a six-point lead. Michigan State improved to 18-4 and is 7-2 in Big Ten Conference play. Indiana and Michigan share the league lead at 7-1 and will meet Saturday.
Michigan State scored the first 14 points of the second half and took the lead for good when Gary Harris hit a 3-pointer 3:44 into the period.
Harris and Denzel Valentine both scored 14 points and Michigan State hit 53 percent of its field goal attempts.
Illinois (15-7, 2-6) was led by Tracy Abrams with 16 points.