Marcus Fuller threw for 312 yards on 22-of-38 passing and Pena rushed for a career-high 112 yards on 25 carries as Brown (4-2, 2-1 Ivy League) jumped out to a 34-10 lead through two quarters. Fuller struck early, hitting Alexander Jette on a 59-yard scoring strike with 14:24 left in the first quarter.
Cornell (0-6, 0-3) battled back to close to 37-24 when Robert Somborn, who finished with 205 yards passing and three touchdowns, passed to Ben Rogers from the 49 for a score with 14:15 left in the game.
Pena, the first Brown player to go over the 100-yard mark this season, ran in from the 1 with 2:49 remaining to seal the win.
Brown has won four consecutive games. The last loss was to Harvard, 53-27, on September 26.