Clement completed 22 of 28 passes for 298 yards and five touchdowns. He also ran 10 times for 79 yards and two touchdowns as the Owls scored the school's most points in a game since 1916.
Dillard caught eight passes for 114 yards overall. He caught one pass from Clement in the first quarter and another two before halftime as the Owls led 56-20 at the break.
Dillard also caught a touchdown pass from Jeramy Goodson.
Rice (3-2) scored two defensive touchdowns in the third quarter and pulled most of its starters in the fourth.
Giovanni Vizza completed 25 of 39 passes for 251 yards and a touchdown for North Texas (0-4), which has given up 219 points.
Rice scored the last 49 points of the game.
The 77 points are the most by a Conference USA team. The old record was 72 by Tulane against Southwestern Louisiana in 1998.
