Junior guard Leo Vincent hit a 3-pointer with 6.2 seconds left in regulation to put the Dawgs up three, but after a series of timeouts senior guard D.J. Balentine hit a three to tie the game and send it to overtime.
In overtime, Evansville shot 4-4 from the floor to close out the game.
Evansville was led by Balentine and junior guard Mislav Brzoja, who each had 25 for the Aces. Beane finished with a game-high 30.
SIU (18-4, 7-2 Missouri Valley Conference) is tied with Evansville (18-4, 7-2 MVC) for second-place and plays next at 3 p.