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.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.