Vanderbilt (19-8, 8-4 Southeastern Conference) stayed one game behind second-place Florida in the league standings.
Gerald Robinson finished with 19 points for Georgia (12-14, 3-9 SEC). The Bulldogs, whose student section was not half full among a sparse crowd for a rare 1 p.m. start, have dropped two straight.
The Commodores hit three of their first five field-goal attempts, but closed the first half by missing 13 of their next 16 to trail 29-28.
Vanderbilt's performance was in stark contrast to their last game, a 102-76 victory Thursday at Mississippi in which the Commodores' point total was their highest in an SEC road game since 1969.
Jenkins, the SEC's leading scorer, buried two consecutive 3s to give the Commodores a 12-point lead, 56-44, their biggest lead thus far, with 6:02 remaining.
But Vanderbilt, which began the game with ranked third in SEC scoring, still finished 17 points below its season average.
Georgia's leading scorer, freshman guard Kentavious Caldwell-Pope, did not take a shot in the first half after picking up his second foul just 4 minutes into the game. He finished with just six points on 3-of-13 shooting.
Dustin Ware was just 2 of 10 from the field, including 1 of 9 on 3-point attempts, to finish with seven points. Georgia, the league's worst scoring team, finished nine points under its average.
Brad Tinsley's 3 in front of the Vanderbilt bench with 2:43 remaining gave the Commodores their biggest lead, 13 points.