The Hawkeyes finished the season with a 7-1-1 record, as in 1957, but this year they would travel to Pasadena to play the Pacific Coast Conference champion California in the Rose Bowl.
In 1958, Fleming helped the Hawkeyes to a 6-0-1 Big Ten clinching victory over the University of Minnesota, and led the team in scoring.
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In 1959, Fleming and the 7-1-1 Hawkeyes defeated the University of California (and Fleming's future BC Lions teammate, quarterback Joe Kapp) 38-12, in the 1959 Rose Bowl.