Goins connected on 10-of-12 free throws for the Volunteers (7-0), who dealt the Panthers their first non-conference home loss in nearly six years.
Tennessee also got 14 points from Cameron Tatum in the victory, in which the Vols jumped off to an early lead and never looked back, shooting 56.3 percent from the field.
The Panthers (10-1) suffered their first loss of the year. They got 21 points, nine assists and five rebounds from Brad Wanamaker. Gilbert Brown and Ashton Gibbs each added 15 points.