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.
Mississippi's football program has been cited for 13 of the 28 NCAA rules infractions included in the notice of allegations that the Rebels received in January.
ESPN Big Ten reporter Brian Bennett discusses why the SEC is upset about Michigan's spring break trip and what the NCAA might do about it.
Stanford and Notre Dame split their last two meetings in dramatic contests, and their 2016 matchup will be highly anticipated.
A lawsuit alleges that the University of Tennessee has violated Title IX policies and created a "hostile sexual environment" through indifference toward sexual assaults by student-athletes.
Ian O'Connor, senior writer at ESPN.com, joins The Paul Finebaum Show to discuss Roger Goodell's response to safety concerns in the NFL.
Stanford defensive line coach Randy Hart is retiring after 46 years as a college coach.