Florida then posted an 8-5 win over the Tigers in the completion of Friday night's game that was suspended due to heavy rain. The Gators held a 7-0 lead when the game resumed in the bottom of the fifth inning.
Florida improved to 30-11 overall, 14-6 in the SEC. LSU is 32-12 overall and 11-9 in conference play.
The teams will meet in Game 3 of the series at 1 p.m. ET Sunday in a contest televised by ESPN.
"I was proud of the way we came back in the suspended game and actually brought the tying run to the plate," said LSU coach Paul Mainieri. "This is a tough place to win, but I know players will give everything they have to win the game tomorrow. There are still a lot of games to be played, and my concern is that we are playing our best once we get into the postseason. We certainly have the ability to get things headed in a positive direction."
LSU rightfielder Mikie Mahtook hit the first pitch of the game from Randall over the left-centerfield fence, giving the Tigers a 1-0 lead.
However, Randall (5-3) was in control the rest of the way, allowing just one run on seven hits in eight innings with one walk and seven strikeouts.
LSU starter Chris Matulis (5-2) was charged with the loss, as he surrendered seven runs on nine hits in four innings with five walks and one strikeout.
Florida tied the game in the second inning against Matulis on a sacrifice fly by leftfielder Jonathan Pigott.
Centerfielder Matt den Dekker's RBI single gave the Gators a 2-1 lead in the third inning. Florida extended the advantage with a pair of runs in the fourth as designated hitter Bryson Smith drew a bases-loaded walk and third baseman Austin Maddox provided an RBI with a fielder's choice grounder.
The Gators added three runs in the fifth on Pigott's RBI double and sacrifice flies by second baseman Josh Adams and shortstop Nolan Fontana.
Leon Landry belted a two-run homer for the Tigers in the top of the ninth, his fourth dinger of the season, to account for the final margin.
The Gators took a 1-0 lead Friday in Game 1 against LSU starter Anthony Ranaudo in the first inning on an RBI single by Maddox.
Florida extended the lead to 4-0 in the second on a three-run homer by Adams, his seventh dinger of the season.
The Gators added three runs in the third against reliever Joey Bourgeois as catcher Mike Zunino ripped a run-scoring single and leftfielder Tyler Thompson lined a two-run triple.
Florida added a run in the fifth when play resumed to increase the lead to 8-0, but LSU erupted for four runs in the top of the sixth against reliever Greg Larson. First baseman Blake Dean and catcher Micah Gibbs delivered RBI singles, designated hitter Matt Gaudet contributed a run-scoring double, and Landry added a fielder's choice groundout to plate a run.
Landry lifted a sacrifice fly in the seventh to narrow the gap to 8-5, but Florida reliever Kevin Chapman blanked the Tigers the rest of the way. Chapman picked up his eighth save as he allowed no hits in 2.2 shutout innings with no walks and two strikeouts.
Florida starter Alex Panteliodis (7-2) earned the win, limiting LSU to no runs on four hits in five innings with no walks and two strikeouts.
Ranaudo (2-2) took the loss as he gave up four runs on six hits in two innings with no walks and no strikeouts.