Smith missed 13 of 17 shots from field but made up for it shooting 12 of 15 from the foul line. Nigel Ribiero added 10 points for Grambling (11-12, 7-3 Southwestern Athletic).
With Grambling leading 69-66, Smith fouled Jared Sam with five seconds left after he converted a layup to reduce Southern's deficit to a point. But Sam missed the potential and-1 chance to tie it and time ran out.
Sam's layup gave Southern a 41-32 lead with 13:32 left. Grambling later went on an 8-0 run and Jackson tied it at 45 with a dunk. The teams traded leads before Jackson made two foul shots for a 61-60 lead that Grambling never gave up. Ribeiro made two fouls shots for a 69-66 lead with 15 second left.
Sam led Southern (9-14, 5-5) with 23 points on 7-of-10 shooting from the field and 9 of 11 from the free throw line and Aaron Ray scored 14.
The rebuilding Wildcats are set to raise the 2018 national championship banner next week -- and also lower expectations for the season to come after multiple NBA departures.
Michigan coach John Beilein can't yell or throw a chest pass yet after his offseason heart surgery, but the coach says he is ready for the upcoming season -- and fully expects to be recovered by that time.
Former Memphis All-American and NBA All-Star Penny Hardaway tipped off his first camp as new coach of the Tigers, and he's "really anxious" to get to work.