The Spartans are tied for first in the Atlantic Sun Conference with Jacksonville and Florida Gulf Coast.
Maxey tallied a career-high 26 points to go with 13 boards. Craig finished with 15 points and 10 rebounds. Ty Greene added 14 points for SC Upstate (13-10, 7-3), which has beaten Lipscomb four consecutive times, including a 98-61 rout Jan. 7.
SC Upstate led 11-9 before Craig hit a 3-pointer to spark a 9-0 run. The Spartans led 32-25 at the break and stretched their lead to as much as 16 in the second half.
Neither team shot well, 32 percent (22 of 68) for SC Upstate compared to 33 percent (23 of 70) for Lipscomb, but the Spartans knocked down a school-record 35 free throws.
Malcolm Smith paced Lipscomb (8-13, 3-7) with 17 points.
Officials: North Carolina must show proof of discrimination-free zone, or lose NCAA tournament games
North Carolina must prove to the NCAA that its host arenas will provide a discrimination-free zone, or risk losing NCAA tournament games in 2017 and 2018, multiple officials told ESPN.
Jalen Rose and David Jacoby examine the new NCAA draft rule and consider how it would have affected "The Fab Five."
Florida and Duke will meet on Dec. 6 in the Jimmy V Classic at Madison Square Garden as one of two high-profile games to help raise funds for cancer research.