Brown (4-3, 1-3) led 17-14 after Cody Taulbee ran one in from 1 yard out with 3:37 left to play.
However, Dexter Davis returned the ensuing kickoff 46 yards and Ragone completed two passes for 15 yards, then ran for another 6 to set up Loftus' game-tying field goal.
Ragone finished with 165 passing yards and 46 rushing yards.
The Bears took over with 2:12 remaining but Trevor Neimann picked off Patrick Donnelly's third pass of the possession, giving the Quakers (3-4, 3-1) the ball on the Brown 44.
Ragone then ran for 17 yards on two carries and completed a 2-yard pass to Eric Fiore to set up Loftus' game-winning 35-yard field goal.
Donnelly completed 30 of 47 passes but threw four interceptions.
Michigan coach Jim Harbaugh says young players at his camps this summer have him convinced that football has a bright future.
GameDay 100: During the Chick-fil-A Bowl in 2013, Texas A&M quarterback Johnny Manziel manages to stay on his feet, scrambling to buy time to complete the touchdown against Duke.
In the dog days of summer, some of the world's most popular sports figures take a crack at sports other than their own.
Kansas State will add experienced safety Dante Barnett to what it appears to be a very solid returning core in the secondary.
On a defense in desperate need of new playmakers, Mondeaux is one of the Ducks' and new DC Brady Hoke's best bets.
Former NFL executive and player Merton Hanks has been named senior associate commissioner of Conference USA. He will be responsible for managing the league's operations for football and baseball.