Polk, who was 7-for-8 from the floor, also grabbed eight rebounds and blocked a shot for the Falcons (1-0). Thomas, who was 4-for-5 from 3-point range, also chipped in five boards and two steals.
Bowling Green actually had trouble shaking the Division II Warriors (0-2), leading just 26-22 with just less than 6 minutes to play in the first half.
But, after a Falcons timeout, Bowling Green went on a 13-0 run from that juncture to take a 17-point lead into the locker room. Polk scored six of his 14 points during the spree.
The Falcons cruised from there, outscoring the Warriors 28-23 in the second half.
Jerry Oden led the Warriors with 16 points and 10 boards.