8, by Howard Griffith of Illinois in 1990
Although one might guess this record came in a one-sided rout of Southern Illinois, SIU actually led 21-7 before the Illini came roaring back to win, 56-21, as Griffith scored all his team’s touchdowns. He scored one TD (5 yards) in the first quarter, three touchdowns in the second quarter (51, 7, 41), and four touchdowns in the third quarter (5, 18, 5, 3). The effort shattered the school's single-game touchdown record of five in a game set by Red Grange in 1924.
Griffith finished his college career with 31 rushing touchdowns before going on to an NFL career in which he earned two Super Bowl rings playing for the Denver Broncos.