The seventh-ranked Buckeyes led by as many as 11 in the second half but had to tough it out late in front of 2,893 at the Pete Maravich Activities Center.
Tayler Hill broke a 53-all tie with a layup with 37 seconds remaining to put the Buckeyes ahead for good.
After LSU's LaSondra Barrett missed the front end of a 1-and-1, Brittany Johnson made a pair of free throws for Ohio State. Latear Easton missed a three-pointer, and Hill secured the rebound before knocking in two more from the charity stripe to set the final margin.
The Buckeyes improved to 3-0 despite missing starting point guard Samantha Prahalis and four injured reserves.
Hill, who continued her fine work in place of Prahalis, the All-Big Ten performer suspended for the first three games because of a secondary NCAA violation, scored 15 points, grabbed seven rebounds and handed out three assists while committing one turnover. For the third game in a row, she played all 40 minutes.
Adrienne Webb led the hosts with 16 points while Latear Eason added 12 for the Tigers, who fell to 0-2 on the season and saw their three-game winning streak in the series snapped.
The Buckeyes improved to 5-5 against the SEC under the guidance of Foster.
Prahalis is due back for Ohio State's next game, a 7 p.m. visit from East Tennessee State on Monday night at Value City Arena in Columbus.
Head coach Jim Foster also hopes to regain the services of guard Amber Stokes (mononucleosis) and center Ashley Adams (knee) soon after the pair returned to practice this week, but when they will be cleared for game action has not been determined.
Another reserve guard, freshman Amy Scullion, is out for the season after right knee surgery and sophomore center Aleksandra Dobranic could be out longterm with a foot ailment.