Mississippi State (15-10, 6-6) saw a 12-point lead dwindle to a single point in the final six minutes. But Rhodes' basket with 1:37 left broke an 11-0 LSU run and the Bulldogs held on from there for a third straight victory and their fourth in five games.
Tasmin Mitchell had 17 points for LSU (14-12, 3-9), which has lost eight of its last nine games. Glen Davis, bothered by the strained right quad muscle, had 14 points for the Tigers and Terry Martin added 10.
Mississippi State took control after Martin's layup gave LSU a quick 30-28 lead to open the second half. The Bulldogs then scored 13 straight points, ending with Reginald Delk's trey that put the Bulldogs up 41-30.
LSU shored up its defense soon after by employing a full-court press. It had to, to stay in the game.
The Tigers didn't surpass 10 points for the second half until Martin's 3-pointer with six minutes to go, which pulled LSU to 49-40. With Mississippi State in the penalty, it started an 11-0 run -- including six made free throws -- that had LSU back in the game at 49-48 with 2:52 left.
MSU went 5:22 late in the half without a point until Rhodes backed into the paint on Davis and hit a twisting shot off the glass to give the Bulldogs a 51-48 lead.
Davis got LSU back within a point, rising powerfully from a crowd close to the hoop to put the ball in off the glass. Gordon was fouled on the other end and missed his second of two free throws with 35 seconds left. But he got the rebound after the ball was tipped out, and the Bulldogs went back to the free throw line and got a pair from Barry Stewart for a 54-50 lead with 26.8 seconds left.
All LSU could answer with from there was a missed 3-pointer from Davis. Mississippi State was able to hit a couple more free throws and run out the clock from there.
An early 14-4 run capped by Stewart's 3-pointer gave Mississippi State a 21-12 lead through the first 10 minutes. Mitchell, who had 13 points in the first half, and Martin both hit a pair of jumpers, including a 3-pointer each, to help LSU close to 26-24. Davis, held to only 3 points in the opening 20 minutes, tied it at 26 from close range after spinning by a defender in the lane. The half ended with the game tied at 28.