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.