PASADENA, Calif. — In mid-August, after prolonged vacillation, Southern California Coach Clay Helton declared the junior Max Browne his starting quarterback. Browne, once a top-ranked recruit, had waited his turn behind Cody Kessler, and the decision generated minimal dissent among Trojans fans.

Three games into the season, Helton changed his mind. Out went Browne, and in came the freshman Sam Darnold. U.S.C. went on a tear, closing out its regular-season schedule with eight consecutive wins.

Darnold tacked an exclamation point onto an improbable debut season on Monday by guiding U.S.C. (10-3) to a pulsating 52-49 Rose Bowl win over Penn State (11-3).

Possessing uncommon mobility for a 6-foot-4 passer and an array of receivers with sprinter speed and flypaper hands, Darnold threw for 453 yards and five touchdowns, including three to Deontay Burnett, in a back-and-forth game that will be remembered as one of the best iterations in the bowl’s 103-year history.