Vanderbilt (18-18, 7-9) will go for its second straight series win over the Tigers when the two teams meet again Saturday at 4 p.m.
Sowers (3-4) allowed just two hits over the first two innings and didn't get into trouble until the seventh inning when LSU finally got a runner into scoring position. By then, the Commodores were already ahead 3-0.
Clay Harris led off the seventh for the Tigers with a walk and advanced to third when Blake Gill doubled to the gap in left. Gill was the only LSU player with more than one hit in the game, and his double was the only extra-base hit for the Tigers.
Quinn Stewart scored Harris with a grounder to short, but Sowers kept the score 3-1 when he retired the next two hitters.
Vanderbilt got the run back in the bottom of the seventh with a two-out RBI single from Ceasar Nicholas.
LSU made the score 4-2 in the eighth inning when Aaron Hill singled to left and the ball got past Jones in the outfield. The miscue allowed Ryan Patterson to come home from second when a clean play from Jones would have kept him at home.
Vanderbilt closer Jensen Lewis replaced Sowers and gave up an infield hit to Ivan Naccarata to put runners on the corners, but Clay Harris hit into an inning-ending double play to end the Tigers' threat.
Lewis sat down LSU in order in the ninth for his sixth save of the season.
Jones started his assault on the Tigers early, touching LSU starter Justin Meier (4-2) for a two-out double. It put runners on second and third for John Kaye, who doubled to right field for a 2-0 Vanderbilt lead.
Zach Simpson doubled against Meier in the second inning, but the LSU freshman rebounded to limit Vanderbilt to two hits over the next three innings.
But LSU could not solve Sowers, allowing the Commodores to win without managing much more offense than the Tigers. Jones gave Vanderbilt a 3-0 with a sixth-inning solo home run to left field.
It was the second straight loss for Meier, who allowed ten hits over seven innings.
Greg Smith pitched the eighth inning for LSU and kept the score at 4-2 despite allowing two hits.