Coastal Carolina made 13 of 20 field goals (65 percent) in the first half while taking a 36-31 lead into the break. Its collective hot hand, however, was left in the locker room.
Winthrop (15-11, 8-5 Big South) limited the Chanticleers to just 6-of-19 shooting, including 1-of-8 from 3-point range, in the second half to take control of the game.
Brown and Smith each scored 10 points after the intermission.
The Eagles used a 9-2 run to take a 44-40 lead with 14:47 to play - their first since 25-23 with 4:25 left in the first half - and a 14-4 run several minutes later gave them a 10 points lead with 48 seconds left.
Warren Gillis scored 25 to lead CCU (16-7, 9-4).