The junior tailback from Sicklerville, N.J., finished with 121 yards on 29 carries, giving the Doak Walker winner as the nation's top running back at least 100 rushing yards in every game this season.
In all, Greene compiled 1,950 yards this season, second-best in the country.
Richard Stanzi completed 13-of-19 passes for 148 yards, one touchdown and two interceptions, while the defense forced five turnovers for the Hawkeyes (9-4), who finished with a four-game winning streak.
Garcia threw three interceptions and lost a fumble in the first half.
South Carolina lost its final three outings, including 56-6 to Florida and 31-14 to archrival Clemson.