Pena's score came on a five-play, 42-yard drive after Princeton's Chad Kanoff was hit while trying to throw and his pass was intercepted by Will Twyman.
Princeton (4-1, 1-1 Ivy) rallied from a 21-7 deficit to tie it twice, the final time at 31-all with 10 minutes left on Kanoff's 10-yard score to Scott Carpenter.
Brown never trailed, taking the lead on the game's first play when Alexander Jette returned the kickoff 99 yards.
The game matched Princeton's league-leading rushing offense against the Ivy's best passing offense of Brown (3-2, 1-1). The teams combined for 924 yards, though Princeton led with 373 yards passing and Brown with 192 rushing.
Brown snapped Princeton's four-game winning streak and beat the Tigers for the first time in four games.