The Racers (21-11) secured a berth in the semifinals behind a terrific offensive effort by their starters.
Payne drained four 3-pointers, Dexter Fields scored all 15 of his points from behind the arc, Jarvis Williams netted 18 and Jonathan Fairell checked in with 13 points, 10 rebounds and four blocks for the victors.
Mike Burwell and Jerrelle Benimon paced Towson (25-11) with 20 and 18 points, respectively, in the final quarterfinal matchup of the tourney.
Yale, VMI and Pacific all advanced on Wednesday.
The Tigers were ahead by a 39-36 count at halftime and it was even at 57-57 at the midway point of the second half before Murray State turned it on.
Fields got things started with consecutive 3-pointers, and it was an seven- point game, 70-63, before an 11-0 run, capped by Payne's deep mark, essentially put the game away.