The Illini (2-0) opened the game red-hot from the field, shooting 60 percent in the first half.
After Coppin State (0-2) hit a three to open the scoring, Illinois went on a 16-0 run and never looked back.
The Illini started 0-for-3 from the field but made 15 of their next 16 shots to put the game out of reach early in the first half.
The 114 points are the most that the Illini have scored under Groce in a non-exhibition game. The previous high was 94, set on Nov. 19, 2012 against USC.
The Illini stretched the lead to 37 in the first half and as many as 62 overall.
It marks the first time that Illinois hit the century mark since Dec. 27, 2005.
Illinois was held to 41.1 percent shooting in its exhibition victory over Quincy on Friday but its offense was ruthlessly efficient against Coppin State. Six players reached double figures and the Illini hit 15 threes for the game.
Illinois: Center Nnanna Egwu continued his slow start to the season. The senior was limited to six points and two rebounds in just 18 minutes of play.
Coppin State: Coppin State allowed over 100 points for the second consecutive game after giving up 107 to Oregon on Friday. The Eagles didn't allow a team over the century mark all last season.
Coppin State travels to Notre Dame on Wednesday.
Illinois hosts Austin Peay on Friday as a part of the Continental Tire Las Vegas Invitational.