The Crusaders (7-5, 5-1) cashed in on four Georgetown turnovers and held the Hoyas (5-6, 1-5) to 44 total rushing yards in earning their automatic bid to the NCAA playoffs.
Connor Degenhardt's 46-yard pass to Ayir Asante set up Cozier's 15-yard TD run in the second quarter. Dobbs intercepted a Gunther Johnson pass on the next series and raced untouched down the sideline for a 14-0 lead.
Derek Ng kicked a 21-yard field goal and Cozier scored on a 20-yard run in the fourth quarter after the Hoyas missed a field goal.
Cozier gained 161 yards on 23 carries. Degenhardt was 10 of 14 for 144 yards passing.
Johnson was 12 of 21 for 121 yards for the Hoyas, who have lost four straight.