Chicago (2-0), which won its first Midway Classic crown since 2002, led 34-19 at the intermission and built its largest lead of the game at 43-23 with 16:13 left to play on a Meyer three-point shot.
Rose-Hulman (1-1) cut the Maroons' lead to single digits, 52-43, at the 5:24 mark when David Yaraschefski sunk a pair of free throws.
The Engineers closed to within five points in the final minute when a jumper by Ron George made the score 57-52 in favor of the Maroons with 27 seconds showing on the clock. Meyer then hit a pair of free throws with 21 seconds remaining to seal the victory.
Clay Carmody was selected as the tournament most valuable player and was joined on the all-tournament team by Jason Hicks.
George paced Rose-Hulman with a game-high 13 points, while Jason Bednarko added 12.