Crockett, deputising for the injured Marshall Faulk, ran for two touchdowns and 147 yards on 13 carries, setting a Colts' post-season record. In the regular season, he had just one carry and gained no yards.
Crockett scored on runs of 33 and 65 yards. "Zack was unbelievable," Jim Harbaugh, the Colts quarterback, said. "It was crazy the way he was running out there. That one 65-yarder was a beautiful thing. You've got to give some credit to our offensive line."
"I just had to stride it out," Crockett, a third-round draft choice from Florida State, said of his 65-yard score. "Some people think a big guy can't run. I had to show them a big guy can run."
Faulk ran for 16 yards on the first play for Indianapolis and left the game later in the series. He was diagnosed as having a bruised left knee and it is not clear whether he will be able to play this weekend.
The Colts' first play-off victory in 24 years ended a run of five play- off defeats and earned them a trip to Kansas City on Sunday. Harbaugh threw two touchdowns and ran for another and finished 16-of-27 for 175 yards, as the Colts became the first AFC team to win a wild card game away from home since Pittsburgh won in Houston in January 1989.
San Diego had won the final five games of the regular season to reach the play-offs. The rookie Aaron Hayden led the Chargers, with 18 carries for 80 yards. Natrone Means was held to 11 yards on six rushes, while Ronnie Harmon had 10 catches for 133 yards. Stan Humphries, was 23-of- 47 for 292 yards, with four interceptions and two touchdown passes.
Earlier in the day, Brett Favre threw for 199 yards and three touchdowns as Green Bay Packers beat the Atlanta Falcons 37-20 in the NFC wild card game.
Edgar Bennett ran for a Green Bay play-off record of 108 yards on 24 carries, beating by three yards the old record shared by the team's legends Jim Taylor and Paul Hornung.
The Packers will travel to San Francisco to play the 49ers, the defending Super Bowl champions, on Saturday.
NFL play-offs: AFC: Indianapolis 35 San Diego 20. NFC: Green Bay 37 Atlanta 20. Divisional play-offs: Saturday: Pittsburgh v Buffalo; San Francisco v Green Bay. Sunday: Dallas v Philadelphia; Kansas City v Indianapolis.Reuse content