Luuk van Bree scored 14 points and grabbed five rebounds for the Braves (3-15, 1-4 Missouri Valley). Callum Barker added 10 points and nine rebounds, Ronnie Suggs had nine points and Antoine Pittman chipped in eight points. Bradley averaged 40 percent shooting from the field and 100 percent from the line.
Thomas sank the game-winning 3-pointer with 13 second to go, capping a 9-2 surge by the Braves that took them from a six-point deficit to lead by one for the win.
Loyola of Chicago led 23-21 at the break and had an 11-point advantage, 39-28, early in the second half.
Devon Turk led the Ramblers (7-10, 0-5) with 15 points and five rebounds.