Payne finished with 7-of-15 shooting from the field and 11-of-13 from the free throw line for the Racers (21-4, 11-0). Sapp hit 8 of 11 from the field and 8 of 8 from the line.
Sapp finished out a close first half with 10 unanswered points in the final 2:50 to give Murray State a 42-26 lead at the break.
Austin Peay's Josh Robinson hit a jumper with 2:40 left in the second half to bring the Governors (7-17, 2-8) to within seven, 71-64, before Payne hit 8 of 8 from the line in the final 1:30 to clinch the win for the Racers.
Khalil Davis led the Governors with 23 points and 11 rebounds.