Green Bay (15-3, 5-0) won its 10th consecutive game, battling back from a second-half deficit to edge UIC (5-14, 0-5).
Sykes spurred a late charge for Green Bay, beginning with a dunk at the 2:38 mark to tie the game at 63. Sykes then hit a 3-pointer to give the Phoenix a 66-63 lead with 1:51 left.
The Flames had a chance to tie the game down 67-64 with 11 seconds remaining, but turned the ball over and Sykes finished with a fast break dunk on the other end to secure the win.
Brown scored 23 for the Phoenix and Sykes had 21.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.