Saint Francis is now 15-9 overall and 7-5 in the Crossroads League.
The Cougars led by as many as 24 points in the second half before Goshen (7-16, 0-12) cut the advantage to as few as five in the closing minutes.
Senior Ethan Hussey had 21 points and junior Scott Kohne finished with his 13th double-double of the season with 21 points and 14 rebounds.
Freshman Kyle Sovine came off the bench to score a career-high 14 points for Saint Francis.
The Cougars will host Taylor on Tuesday at 7 p.m. The Troans upset No. 12 Bethel College on Saturday.