UCLA took a 3-3-1 record into its game against the 8-0 Trojans, who were ranked fourth by Associated Press and second in another national poll.
"I don't think anyone gave us much of a chance," Kilmer said Tuesday by phone from his home in Fort Lauderdale, Fla.
The defeat ended USC's hopes for a national title, which would have been a consolation prize of sorts for a team that was ineligible for the Rose Bowl because of an NCAA penalty.
"We went into the game and started overlooking the Bruins because they didn't look like they had very much," Marlin McKeever, an All-American end for the Trojans, said Tuesday.
Kilmer, who played wingback for the Bruins, suffered a hairline ankle fracture the week before the game against the Trojans when he was struck by a baseball while umpiring a game on campus.
Kilmer tried to practice but could not run because of the pain. So trainer Ducky Drake summoned Kilmer to the gymnasium to run in basketball shoes.
The next day, Kilmer was fitted with a newfangled rubber shoe.
"They were ripple soled, like the first Astroturf shoes," Kilmer said. "I don't know where they got them, but they felt good on my feet."
Kilmer sat out the first half against USC, but came on in the third quarter with the Bruins trailing, 3-0.
"One play, it was fourth and 10, and I hobbled for a first down," Kilmer said. "I remember [USC's] Mike McKeever screaming, 'A guy with a broken leg is running for the first down!' "
Ivory Jones tied the score with a 31-yard field goal early in the fourth quarter, setting the stage for the key play of the game.
Facing a second-and-17 on the UCLA 47, Kilmer received the snap and passed the ball downfield, where USC's Willie Wood and Jerry Traynham were defending UCLA's Marvin Luster. The three players leaped for the ball and Wood came down with it at the Trojan seven for an apparent interception.
An official, however, called pass interference against the Trojans, giving the Bruins life.
Three plays later, UCLA halfback Ray Smith ran for a touchdown that gave UCLA a 10-3 lead with 8:06 left.