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.
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.