Karrash's kick saved the day for the Quakers (3-4, 1-3 Ivy League), who saw a 35-19 third-quarter lead turn into a 36-35 deficit with 8:40 left to play.
EJ Perry's 50-yard touchdown run gave the Bears (1-6, 0-4) a 7-0 lead after one quarter.
Abe Williams capped back-to-back drives with TD runs of 1 and 8 yards to put Penn up 14-7 with 5:19 left before halftime. Perry scored on a 3-yard run, but the point-after kick missed and Brown trailed 14-13. Nick Robinson connected with Ryan Cragun for a 24-yard scoring strike with 2:09 left, giving Penn a 21-13 lead, but Perry found Jakob Prall for a 37-yard score. The 2-point try failed and left Brown trailing 21-19 at halftime.
Penn stretched its lead to 35-19 just 2 minutes into the third quarter. Robinson had an 11-yard TD pass to Rory Starkey Jr. and on the ensuing kickoff Brian O'Neill scooped up a fumble and raced 21 yards for a TD.
Brown pulled within 35-22 after three quarters on Dawson Goepferich's 24-yard field goal. The Bears got within six points on Allen Smith's 1-yard TD run and grabbed a one-point lead on Perry's third TD run of the game, a 16-yarder with 8:40 remaining.
Robinson completed 19 of 33 passes for 247 yards, two TDs and an interception. Cragun had a career-best 11 catches for a career-high 144 yards.
Perry had 24 carries for 117 of Brown's 245 yards on the ground. Perry completed 20 of 37 passes for 225 yards with two picks. Smith added 83 yards on 15 totes.
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