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 Nation had nine points and six assists for James Madison, and Devon Moore added nine points and five assists.
Andre Smith led the way for Winthrop, scoring 26 points and making 4 of 6 from 3-point range.
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