Despite the loss, LSU (25-13-1, 11-5-1) remains in first place in the SEC, one-half game ahead of Arkansas and Auburn.
Vanderbilt (19-18, 8-9), which trails SEC East leader South Carolina by one game, has already won its second consecutive series over LSU for the first time in school history and goes for the sweep on Easter Sunday at 1 p.m.
Although LSU starter Bo Pettit had thrown eight consecutive shutout innings after giving up four runs with two out in the first, Tiger coach Smoke Laval elected to pull Pettit for the 10th inning after he had thrown 117 pitches.
Tompkins walked leadoff hitter Klosterman that set up a potential double play if Tompkins could get a ground ball, but Matt Zeller hit a slow roller on which the Tigers could only retire pinch runner Rucker Taylor at third base.
Nicolas then lined a 1-1 pitch to left field, and the throw home from Bruce Sprowl, was cut off as Klosterman came across the plate.
For the second straight game, LSU, which had been limited to one run on one hit through the first six innings by Commodore starter Robert Ransom, finally began to show signs of life in the seventh.
Blake Gill and Clay Harris started the inning with back-to-back singles to place runners on the corners for Ryan Patterson, who blooped a single into short left-center between three Commodore fielders to score Gill and make it a 4-2 game.
Reliever Ryan Buschmann gave up a ground ball single to Jon Zeringue to load the bases. On the hit, Vanderbilt left fielder Warner Jones overran the ball, allowing Harris to score from third, but when Zeringue tried to take second, Jones threw him out on a very close play.
With Patterson on third, Matt Liuzza grounded back to the mound for the second out, but Sprowl grounded a single between first and second to tie the game.
Pettit fell behind 1-0 with two out in the bottom of the first when Nicolas launched his fifth home run of the year over the 35-foot green monster in left field.
Pettit then gave up a single to Jones and walked John Kaye before Tony Mansolino launched the first pitch he saw from Pettit well over the 375-foot marker for a three-run home run to extend the Vanderbilt lead to 4-0.
Following the home run, Pettit settled into a groove, allowing just three hits and one walk over the next eight innings, with only one Commodore runner getting as far as second base. The nine-inning effort tied a career high for Pettit, although he took a no decision for the first time in eight starts this year.
The first two LSU batters of the game, Sprowl and J.C. Holt, drew walks from Ransom to give the Tigers the first scoring opportunity. But Aaron Hill, the Tigers' leading hitter, grounded into a double play to before Ivan Naccarata swung at a high fastball to strike out and end the inning.
The Tigers (No. 7 Collegiate Baseball, No. 10 Baseball America, No. 12 ESPN/USA Today) had similar opportunities in the third and fourth innings also wiped out by double plays. LSU didn't collect its first hit until Patterson's double with one out in the fifth.
Sprowl led off the sixth and reached second base when Commodore center fielder Matt Zeller dropped his easy fly ball. Two batters later, Sprowl scored LSU's first run on a sacrifice fly by Hill.