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.
Kevin Weidl and Marcus Spears look at the best fit, biggest surprise and best player left from the SEC after the first round of the 2016 NFL Draft.
13 minutes before the draft began, Laremy Tunsil's Twitter account was reportedly hacked and a video of Tunsil smoking surfaced. The drama didn't end there as the 13th overall pick dominated the headlines on draft night.
SEC Network checks into Mississippi State's spring football practice for a sneak peak at their offseason adjustments.
Kevin Weidl and Marcus Spears look at how former Ole Miss players Laquon Treadwell and Robert Nkemdiche will fit with the Vikings and Cardinals, respectively.
SEC Network's Peter Burns talks with Seattle Seahawks' 31st overall pick Germain Ifedi about the feeling of being drafted and his excitement for Seattle.
SEC Network's Peter Burns talks with Indianapolis Colts' 18th pick Ryan Kelly about his experience in the NFL draft and thoughts on playing in the NFL.