The Tigers (33-20) dropped their second straight game and have lost three out of the last four meetings against Rice.
The Owls (43-10) have won 22 out of their last 23 games and travel to Marshall for a three-game series this weekend.
LSU heads into its final SEC series of the season at Florida this weekend.
Game times are scheduled for 5:30 p.m. CT Thursday, 5:30 p.m. CT Friday and 3
p.m. CT Saturday. Saturday's contest will be broadcast on Fox Sports Net (Cable
Ch. 38 in Baton Rouge).
LSU holds a one-half game lead over Mississippi State and Tennessee for the final berth in the eight-team SEC Tournament, which begins May 24 in Hoover, Ala.
Three Rice pitchers combined to limit the Tigers to four hits on Wednesday. LSU catcher Robert Lara finished 2-for-4 with a run scored, and right fielder Quinn Stewart connected for his nation-leading 22nd homer of the season.
"You still have to get more than four hits in the ballgame," said LSU coach Smoke Laval. "We got a homer. We got all the runs in that one inning, and we only put pressure on them one time."
The Tigers controlled the game through the first six innings, using solid outings from senior Chris Cahill and freshman Louis Coleman. Cahill fought threw a bases-loaded jam in the second without allowing a run, and he yielded to Coleman to start the fourth.
Coleman inherited an early lead after the Tigers pushed across three runs in the third against Rice starter Will McDaniel. Lara, making only his 10th start of the year, crushed his first career triple to the left field wall to lead off the frame. Left fielder Bruce Sprowl then gave LSU a 1-0 lead with a single through the middle.
Three batters later, Stewart launched a towering, two-run, shot over the left-centerfield wall to move him into a tie with James Madison's Kellen Kulbacki for the national lead.
Meanwhile, Coleman and Cahill combined to limit the Conference USA champions to four hits until Jonathan Wilhite entered in the seventh.
Wilhite allowed back-to-back singles to left fielder Aaron Luna and designated hitter Kenny Ford to lead off the seventh. Freshman Darryl Shaffer inherited both runners and immediately surrendered the lead when centerfielder Tyler Henley drilled a three-run homer to right to tie the game at three apiece.
Rice nearly took the lead in the eighth when Sprowl committed the first error of his career. Sprowl, who was errorless in 168 consecutive games, dropped a fly ball off the bat of first baseman Joe Savery to start the eighth.
However, Sprowl atoned for the error when he made a leaping grab on a liner from Luna to keep the go-ahead run from scoring with two outs.
Sprowl attempted to spark LSU with a run in its half of the eighth with a leadoff walk. But Mayer failed at a sacrifice bunt attempt before striking out and Wise followed with another strikeout. Waguespack then grounded out to end the inning.
Chase Dardar came into work the ninth and allowed the first two batters to reach on a single and a double. Friday, who was previously 0-for-4, then lined a two-run single through the middle with the infield drawn in. Dardar later allowed Friday to score on a wild pitch to account for the final margin.
Rice left-hander Bobby Bramhall and right-hander Bryce Cox combined to toss five hitless innings. Cox (2-1) was credited with the win, issuing no runs on no hits while striking out four.
Dardar (5-3) suffered the loss, giving up three runs, walking one and striking out one.
"The pitching was adequate," said Laval. "It was good enough (to win). I wanted to see Coleman and Dardar back out there but not when you only get four hits."