The Illini held on when Matthew Butler's desperation heave at the buzzer was short.
The Skyhawks forced Illini turnovers on consecutive possessions to cut the lead to 76-72 with 1:08 left.
After an Illinois free throw, Fatodd Lewis made a layup to cut the lead to three.
Black and Aaron Jordan scored four points each during a 14-4 run that put the Illini (2-0) up 65-51 with 7:34 to go.
The Skyhawks scored 14 straight points after Illinois took an 18-point lead early in the second half.
DelFincko Bogan scored eight points during the run, which cut the Illini lead to 51-47 with 13:20 remaining.
Bogan, who came off the bench, led Tennessee-Martin (0-2) with 23 points, six assists and seven steals. Butler added 16 points for the Skyhawks.
Freshman guard Mark Smith had 13 points for Illinois.
The Illini were 19-for-27 from the free-throw line, two days after making 34 of 37 from the line in a 102-55 rout of Southern on Friday.
The Illini continued to struggle from long range.
Illinois, which was 4-for-21 from beyond the arc in Friday's win, made 6 of 21 on Sunday.
Tennessee-Martin didn't score for the first 4:24 of the game, but scored seven straight points over the next minute to go up 7-4.
Illinois retook the lead and gradually pulled away, taking a 44-29 lead at halftime.
Black was 5-for-6 in the first half.