The Huskies had an 11-point lead midway through the second half, but the Tigers brought it back to just three points, 67-64, when Christian Williams hit a 3-pointer with 6:12 left.
Wilcox then hit a 3-pointer with 5:45 left to lift the Huskies (6-4).
Suggs, coming off a career-high 24 points Thursday against Seattle University, scored nine of his points in the second half, including nine of the Huskies first 14 points to start the half.
Kelsey Howard had 23 points for the Tigers.
For Jackson State (0-8), this was the eighth of 11 consecutive road games to start the season. This was their closest loss as they have an average deficit of 24.4 points per game.
The Tigers' first home game - and their Southwestern Athletic Conference opener - will be Jan. 6 against Alcorn State
Jackson State gave the Huskies some early first-half trouble, coming back from seven down to pull to within two points, 13-11, with 14 minutes left. Suggs and Wilcox then hit successive 3-pointers to begin a 14-point Husky run. The Tigers went 5:09 without a point.
The Huskies built the lead to 16 points, 29-13, with just under eight minutes left before the Tigers charged back. Christian Williams connected on a pair of treys to bring the Tigers to within seven, 29-22, at the 7:08 mark.
The lead dwindled down to just two points, 33-31, on Sydney Coleman's fast-break layin before the Huskies used a corrective timeout.
Aziz N'Diaye's rebound put-back with four seconds left gave the Huskies a 40-34 lead at intermission.
The Huskies made just 12 of 26 free throws.