The senior Rawlings became Yale's all-time career leader in touchdown completions when he threw a 33-yard score to Reed Kublink to break a 13-all tie with two seconds left before halftime.
Nick Robinson led a 12-play, 82-yard drive to start the third, and Penn tied it at 20 when he found Rory Starkey Jr. on a 7-yard pass. Dudek later scored on a 2-yard run and the failed 2-point conversion left the score 26-20. Abe Willows scored before the end of the quarter to give the Quakers their only lead of the game, 27-26.
Yale (5-1, 2-1 Ivy League) scored twice in a three-minute span to start the fourth and held off Penn (2-4, 0-3) from there.
Robinson's 20-yard scoring pass to Willows narrowed Penn's deficit to 46-41 with 59 seconds to play, but Yale recovered the onside kick and ended the game.
Rawlings threw for 388 yards and two touchdowns and rushed for two scores. He ran for 67 yards on seven attempts. Dudek had 22 carries for 97 yards.
Robinson threw for 395 yards and three touchdowns. Karekin Brooks had 72 yards rushing on 20 carries and a touchdown and Willows had two rushing touchdowns. Ryan Cragun caught 13 passes for 208 yards.
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