Jarvis Williams scored 13 points with 13 rebounds, Jonathan Fairell had 14 boards, and Payne had six assists for the Racers (17-4, 7-0), the only undefeated Ohio Valley Conference team.
The lead changed hands six times until Murray State's Jeffrey Moss tied it at 31 with a 3-pointer with three seconds to play in the first half.
Payne scored seven straight and Murray State led 50-45 in the second half, but the Cougars pulled within 53-51 on a free throw by Donivine Stewart with 5:22 left. The Racers pulled away on layups by Moss and Payne, but the Cougars again closed within three until Williams hit three free throws in the final 15 seconds.
Kris Davis led the Cougars (8-11, 4-4) with 10 points and Keaton Jackson blocked three shots.
