Payne, who was 4 of 7 from long range, made 10 of 19 field goal attempts and also had eight assists for Murray State (6-4).
Evansville (7-2) took a 62-61 lead with 8:00 left. The Racers' Justin Seymour nailed two 3-pointers and Payne knocked down another to regain the advantage70-63 with 6:57 left and never trailed again.
Evansville's D. J. Balentine, 31 points, made four straight free throws to tie at 79 with six seconds left, but Jonathan Fairell drove for a layup and the win.
T.J. Sapp hit 3 of 5 from beyond the arc to score 15 points and Seymour was good on all three attempts from long range for 10 as the Racers made 11 of 19 3-point attempts.