Harper attended high school in Royal Oak, Michigan, before enrolling at the University of Michigan in 1956. He played football for the Michigan Wolverines football team from 1957 to 1959. As a junior, Harper appeared in 7 of 9 games for the 1958 Michigan Wolverines football team, three of them as the starting left halfback. He was Michigan's leading rusher in 1958, totaling 309 rushing yards, 137 receiving yards, 131 passing yards, 60 kickoff return yards and 33 punt return yards. Playing against Minnesota in October 1958, Harper ran 58 yards for the game-winning touchdown on the first play of the second half. Harper also handled punting duties for Michigan; he had a 61-yard punt against Michigan State in October 1958. As a senior, Harper started all nine games at the left halfback position for the 1959 Michigan Wolverines football team. In the third quarter of the October 1959 game against Minnesota, Harper caught a punt at Michigan's 17-yard line and returned it 83 yards for the game's first points. The return set the Michigan record for the longest punt return, a record which stood until 1972 when David Brown returned a punt 88 yards. During the 1959 season, Harper rushed for 224 yards and also contributed 101 yards on punt returns and 62 yards on kickoff returns.
Buffalo Bills
Harper was selected by the Detroit Lions in the 15th round of the 1960 NFL Draft. He signed instead with the Buffalo Bills in the newly formed American Football League. Harper played as a halfback and placekicker for the 1960 Buffalo Bills and led the AFL with 10 extra points. At 2:08 p.m. on Sunday, September 11, 1960, Harper made the opening kickoff in the first regular-season game in the history of the Buffalo Bills. He also scored "the first official points" in Bills' history on a field goal from the 35-yard line. After taking a 3-0 lead on Harper's field goal, Buffalo did not score again and lost by a score of 27-3 to the New York Titans. In the Bill's second game on September 18, 1960, Harper successfully converted the Bills' first extra point kick after Wray Carlton ran for the team's first touchdown. Playing against the Los Angeles Chargers on October 2, 1960, Harper kicked the second field goal in team history.