The Falcons (10-11, 5-2) fell behind 12-2 at the start but rallied to lead 34-31 at the half.
Eastern Michigan (5-15, 2-5) took its only lead of the second half, 46-45, on Brandon Bowdry's layup with 12:36 remaining. Bowdry led the Eagles with 24 points and 15 rebounds.
A jumper by Thomas 26 seconds later put Bowling Green ahead to stay and began a 17-8 Falcons run for a 62-54 advantage.
Bowling Green led 67-58 with 34 seconds left. A three-point play by Bowdry and two free throws by Antonio Green made it 67-63 with 13 seconds left, but the Eagles got no closer.
Jay Higgins had 15 points for Eastern Michigan.