The Bulldogs were within three points early in the fourth quarter but Lee drove LSU 80 yards, completing all five attempts on the march. His 19-yard touchdown throw to Rueben Randle with 11:56 remaining put the Tigers in front 16-6.
Drew Alleman kicked a field goal in each quarter for LSU ranging from 21 to 42 yards.
LSU (3-0, 1-0 Southeastern Conference) held the Bulldogs to 187 yards and limited them to 2.8 yards per play. Mississippi State managed only 80 rushing yards on 29 carries. The Bulldogs had gained 1,176 yards during their first two contests.
Lee completed 21-of-27 passes for 213 yards. He had a streak of 131 passes without an interception snapped in the second half.
Mississippi State's Chris Relf was 11-of-17 for 96 yards and was benched in the second half. The Bulldogs fell to 1-2, with both losses having come in conference action.