"It's good that we've got guys that can come in and contribute," Harris said of the four other players who scored in double figures.
Vincent Yarbrough scored 19 points, while C.J. Black had 16 and Ron Slay 12. Terrence Woods, who was 3-of-3 from 3-point range, finished with 11 points.
Georgia (9-14, 2-8) held their final lead at 26-23 on Anthony Evans' basket with 6:45 left in the first half.
The Vols turned up the defensive pressure and outscored the Bulldogs 21-12 over the rest of the half. Yarbrough scored eight points in a three-minute span, including a tip-in at the buzzer, that gave the Vols a 44-38 lead.
The Vols extended the lead to 59-44 on Harris' 3-pointer with 15:44 remaining.
On the strength of eight 3-pointers in the second half, the Vols came up with their highest point total of the season.
"The first half was disappointing," Tennessee coach Jerry Green said. "But we picked it up in the second half."
D.A. Layne scored a career-high 30 points to lead Georgia, while Shon Coleman had 25 points and 15 rebounds.
"Tennessee shot the ball well tonight," Georgia coach Jim Harrick said. "I'm happy for Jerry. He has a quality team."
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