The Commodores won despite a sloppy performance saved mostly by going 23 of 26 at the free-throw line in the second half.
South Carolina (10-17, 2-11) was held to a season-low in points as the Gamecocks lost for the seventh time in eight games.
Festus Ezeli added 14 points and blocked four shots, and Lance Goulbourne added 12 points. Jeffery Taylor, the SEC's second-leading scorer averaging 17.8 points, had a season-low four.
Bruce Ellington led the Gamecocks with 15 points, and Damontre Harris had 10.
The Commodores looked tired and struggled shooting throughout. They went cold in the first half after consecutive 3-pointers by Jenkins, the last with 12:06 left, and didn't score again until Brad Tinsley's layup with 7:25 to go.
Ellington got going, hitting back-to-back 3-pointers himself. He then drove for a layup for his first eight points of the game and South Carolina's final eight of the first half. That layup tied up Vanderbilt for the third time in the half at 22.
The Commodores couldn't even get off a decent shot after taking a timeout to set it up with 33 seconds remaining. Goulbourne lost the ball, chased it down and then threw up a shot that came nowhere close to the basket. The sequence was so sloppy a couple of boos were heard.
The lead went back and forth in the opening half with South Carolina holding its last lead at 27-26 on a pair of free throws by Harris. Then Taylor, who missed his first six shots, finally scored off a lob from Tinsley with 17:11 left. That put Vanderbilt ahead with the sixth and final lead change and starting an 11-3 spurt.
Jenkins hit a 3 and had a pair of free throws for a 37-30 lead that was the Commodores' largest with 14:12 left.
The Gamecocks never got closer than three the rest of the way as Vanderbilt kept going to the free-throw line after hitting both attempts in the first half.