Joab Jerome had a game-high eight rebounds to help Winthrop (9-11, 3-5) outrebound Coastal Carolina 39-27.
On top 40-36 with 8:32 left to play, Winthrop went on a 10-2 run to take a 51-38 lead with 5:31 remaining. Smith and Henry made back-to-back 3-pointers during the stretch.
Badou Diagne's 3-pointer for Coastal Carolina cut the deficit to seven, 55-48 at the 2:38 mark, but Smith answered with his fourth 3-pointer to make it a double-digit game, 58-48, with 2:01 to play. Coastal Carolina failed to score again.
The Eagles held the Chanticleers to just 33.3 percent (8 of 24) in the second half.
Anthony Raffa led Coastal Carolina (9-10, 4-4) with 16 points, but scored only two points after the intermission.