Tiger centerfielder J.C. Holt fielded Kaplan's hit in time for a throw to the plate, and Swackhamer slid to the side to avoid a tag from LSU catcher Dustin Weaver. Swackhamer missed the plate on his slide, but Weaver dropped the ball before he could apply the second-chance tag.
The loss ended a five-game winning streak for LSU (11-7). The Tigers will begin Southeastern Conference play this weekend when Florida (13-3) visits Alex Box Stadium.
"We can control how we react (to the loss)," said LSU head coach Smoke Laval. "We need to try and come back and get some wins this weekend. We can control that. We need to bounce back and not get too down."
LSU built a 4-0 lead against Tulane but unearned runs allowed the Green Wave to tie the game.
The Tigers scored their first run in the fourth inning on Blake Gill's bases-loaded sacrifice fly to deep left field.
LSU added to its lead in the fifth. With two outs, Ryan Patterson doubled into shallow center field, just out of the reach of a diving Kaplan am Holt ripped a single into left field to bring him in.
Tulane mounted its comeback in the bottom of the inning. It appeared Tommy Manzella hit right into a double play, but Hill bobbled the ball on a toss to second and all runners were safe for loaded bases.
Bumstead walked in another run on his first batter and was pulled for freshman left-hander Greg Smith, who walked in Tulane's third run but got out of the inning with the Tigers still holding a one-run lead..
"Obviously the bases on balls hurt us," said Laval. "We hit some hard shots right at them, but that's a baseball game. Tulane's a great ball club and they battled through (all the hits), and we have to see how we react to this."
Tulane tied the score in the seventh inning on an RBI triple by Manzella.
Laval went to his bullpen one more time to bring in lefty Billy Sadler, who got the Tigers out of the seventh and faced the minimum through the tenth inning
But Tulane reliever Joey Charron (1-2) was just as good in picking up his first win of the season. The right-hander who normally sees short duty as the Green Wave's closer pitched the last 4.1 innings. He gave up two hits and four walks and struck out four.
Although this was Charron's first decision against LSU, he has a 1.31 ERA in 16.3 innings against LSU and has given up 13 hits to the Tigers over the last three seasons in recording two saves.
LSU had a huge opportunity to take the lead in the tenth, loading the bases with only one out, but Sprowl hit into a fielder's choice at home plate and Weaver flied out to end the threat.
Sadler (1-1) took the loss for the Tigers. He lasted 3.2 innings and struck out four, walked two, and only gave up one hit - the game winner.
"It was a good college ball game," said Laval. "It could have gone either way."