Goins scored six points during a 12-0 second-half run that gave the Dukes (2-5) a 54-34 lead with 9 minutes remaining.
The Eagles (2-4) never got closer than eight points after that.
Winthrop led 21-13 in the first half after a 3-pointer by Derrick Henry. But James Madison responded with a 15-3 run to lead 28-24 with 5:04 left until halftime. Semenov scored five points, and Goins and Charles Cooke each made three-point plays during the Dukes' rally.
Andre Smith led the way for Winthrop, scoring 26 points and making 4 of 6 from 3-point range.
Maryland point guard Melo Trimble has withdrawn from the NBA draft and will return to College Park for his junior season, sources told ESPN.
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.