McCree's 3-pointer sparked a 13-6 run capped by Luckett's dunk and the Bulldogs pulled away 93-85, then Dayon Griffin dunked for good measure.
McCree scored 25 points with 11 rebounds and Luckett had 21 for the Bulldogs (6-1), who were outshot 50-28 in the paint but made 37 of 44 free throws. Qiydar Davis scored 17 points with 14 rebounds and Alex Hamilton added 13 points.
Jackson State led 78-76 in OT after Raeford Worsham's layup, but Davis' layup tied it. Trailing 37-33 at halftime, Jackson State's Paris Collins made two free throws to tie it at 72 at the end of regulation.
Collins led the Tigers (3-6) with a career-high 25 points with 10 rebounds. Javeres Brent scored 20 with six 3-pointers, Chace Franklin scored 18 points with a career-high six assists and Worsham scored 13.