The Phoenix (5-3) overcame an early 8-0 deficit and climbed back to take the lead on a Carrington Love 3-pointer, which sparked a 10-0 run to make the score 60-52 midway through the second half.
South Dakota (3-6) cut the lead to three multiple times, but couldn't pull any closer. A Trey Norris three-point play made the score 86-83 with 19 seconds left, but Green Bay countered with a Greg Mays dunk. Sykes hit a free throw following a Brandon Bos layup for the final margin.
Green Bay had five players score in double figures. Mays scored 15 points, and Jordan Fouse finished with 11 and 14 boards.
Bos scored 19 points, and Trevor Gruis contributed 16 with eight rebounds to lead the Coyotes.
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point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.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.