Rakeem Cato threw four touchdown passes, Devon Johnson rushed for 199 yards and a score and No. 21 Marshall beat Rice 41-14 on Saturday.
Marshall improved to 10-0 for the first time since it finished 13-0 in 1999.
The Thundering Herd (6-0 Conference USA) limited Rice to 180 yards and ended the Owls' six-game winning streak.
Cato had scoring tosses of 2, 25, 30 and 7 yards to give him 117 for his career, surpassing Chad Pennington's school record of 115 set from 1995-1999.
Rice (6-4, 4-2) entered the game allowing an average of only 135 yards on the ground, but Marshall had that matched by halftime. Johnson went over 100 yards for the eighth time this season since converting from tight end in preseason camp.