Holy Cross (2-5) answered with a 21-yard touchdown pass from Peter Pujals to Kalif Raymond, but Connor Fitzgerald missed on a 39-yard field goal attempt four plays later, setting up Brown for the go-ahead score.
Strachan finished with 98 yards receiving and three touchdowns, two of those coming in the third quarter to help the Bears go up 14-7. Fuller was 20 of 37 for 240 yards and two touchdowns.
The Crusaders erased a 17-7 fourth-quarter deficit with a Fitzgerald field goal and a 1-yard run by Gabe Guild with 1:20 left to force overtime. Pujals threw for 252 yards with a touchdown and two interceptions.