Burrow threw his record-setting 29th passing touchdown of the season during the second half Saturday, putting the No. 2-ranked Tigers ahead of Mississippi State 36-7 in an eventual 36-13 win.
Matt Mauk set the previous record of 28 in 2003. JaMarcus Russell then tied it in 2006.
Burrow finished the game 25-of-32 for 327 yards and four TDs in the win. The senior transferred to LSU from Ohio State last season.
He and new passing game coordinator Joe Brady have helped lead an offensive transformation in Baton Rouge this season which has seen LSU rise all the way No. 1 in the country in scoring entering the weekend with 52.5 points per game.
LSU hosts No. 11 Auburn next Saturday. Following a bye week, the Tigers will travel to No. 1 Alabama on Nov. 9.