A basket by D.J. Balentine gave Evansville a 70-66 lead with a minute left. Milton Doyle hit a 3-pointer to get the Ramblers (12-3, 2-1 Missouri Valley) within a point with 42 seconds remaining. Balentine missed a jumper with 12 seconds left and Thomas, getting the offensive rebound after Doyle missed a jumper, scored the winner.
Doyle added 13 points for the Ramblers, who shot 50.9 percent and made eight 3-pointers.
Balentine led the Evansville (11-4, 1-2) with 18 points. Duane Gibson added 16. Evansville shot 57.4 percent, but made just 1 of 7 3-pointers.
Neither team led by more than six.
It was the first MVC road victory for the Ramblers after dropping 10 away games since joining the conference last season.