Vanderbilt remains in seventh place in the race for the SEC Tournament. The Commodores are three games behind Florida and LSU for the fifth and sixth spots, and one game ahead of Tennessee and two ahead of Auburn. The top eight teams will qualify for the five-day tournament, May 26-30.
The 35 wins matched the school record for regular-season victories, set by the 1985 squad.
Klosterman wasted little time to begin his three-RBI day by depositing LSU starter Nate Bumstead's fourth pitch of the game into the left field bleachers for a lead-off home run.
The Commodores homered again to lead off the top half of the second as Cesar Nicolas took Bumstead's first pitch over the left field wall to make it a 2-0 contest. It was his team-leading 11th of the season.
Nicolas finished the game 2-for-4 with two RBI and one run.
Meanwhile, Buschmann handcuffed the Tigers early thanks to a pair of outstanding defensive plays by Klosterman and third baseman Tony Mansolino. Both made diving stops to retire the speedy J.C. Holt in the third and fifth, preventing the Tigers to create any kind of scoring threat.
At 2:11 p.m., a steady rain began to fall, forcing the umpires to postpone the game with Vanderbilt batting in the top of the sixth with a runner at second and no outs.
Freshman Clay Dirks came on in relief of Bumstead after a 1 hour, 35 minute rain delay as play resumed at 3:46 p.m. Dirks immediately fell into trouble, allowing Antoan Richardson to reach on a 1-2 bunt single, moving Klosterman over to third.
Warner Jones followed and knocked in his third run of the weekend, grounding out to shortstop Blake Gill. The run closed the book on Bumstead (8-3) who allowed three runs -- all earned -- on six hits, while fanning four over five innings.
Nicolas closed out the two-run sixth, lining a run-scoring single into left field for his second RBI of the game.
Buschmann, unfazed by the rain delay, came out in the sixth and picked up right where he left off. He fanned Jon Zeringue, the conference's leading hitter, for the third time in the game.
The sophomore right-hander surrendered just three hits the rest of the way, working a perfect ninth to secure his first complete game. He allowed just one extra base hit, that coming off of the bat of Matt Liuzza in the fifth.
Buschmann (7-1) became the first opposing pitcher to hurl a complete-game shutout against the Tigers this season.
Vanderbilt out-hit LSU 12-6.
Vanderbilt will return to action on Wednesday, May 19, when it plays host to Middle Tennessee. First pitch at Charles Hawkins Field is set for 6 p.m.