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.
After a season that saw his shooting numbers slip, should Nigel Hayes return for his senior year at Wisconsin or take the gamble to put him name in this year's NBA draft?
Isaiah Taylor talks about his decision to declare for the NBA draft and what he will miss most about Texas.
Chattanooga women's basketball coach Jim Foster has received a one-year contract extension, the same day the school gave the men's coach a two-year extension.