Allen played college baseball for the Boilermakers, where he twice named Team MVP. A winner of 6 varsity letters, Allen was also a quarterback on the football team, selected as Team MVP in 1960. He platooned at quarterback in 1959, leading the Boilermakers to a 5-2-2 record and six weeks in the Top 15. Earning the starting job in 1960, Allen led the Boilermakers to a record of 4-4-1 and wins over #12 Notre Dame, Ohio State and #1 Minnesota, the AP and UPINational Champion. The Minnesota and Notre Dame wins were both road wins, while the win over Ohio State earned Allen Sports Illustrated's Offensive back of the Week. Purdue spent 5 weeks in the Top 15 and finished the season at #19. Allen was selected for the Blue–Gray Game; throwing 3 touchdowns and led the Blue squad to a 35-7 victory over the Gray squad, quarterbacked by Fran Tarkenton. Allen was the leading passer for Purdue during the 1959 and 1960 seasons and was also the team leader in total offense. He was selected as an All-American shortstop in, he signed with the Twins and played 80 games for Class A Charlotte before being promoted to Major League Baseball. He spent the 1963 off-season as an assistant football coach under Jack Mollenkopf, where he tutored a young Bob Griese. In 1999, he was selected for induction in the Purdue Intercollegiate Athletics Hall of Fame.
Major League career
On Opening Day, April 10, 1962, Allen made his debut for the Minnesota Twins at second base. He was put into a position vacated by Billy Martin a week earlier. Allen had one hit in four at-bats on opening day. His rookie performance led to a selection to the 1962 Topps All-Star Rookie Roster and finished 3rd in Rookie of the Year voting, finishing behind Tom Tresh and Buck Rodgers. Allen played five seasons for the Twins and was traded to the Washington Senators with pitcher Camilo Pascual for pitcher Ron Kline. After five seasons in Washington, the Senators moved to Texas and traded him to the New York Yankees. Allen played for New York in 1972, backing up second and third base. He played 17 games for the Yankees in 1973 before being purchased by Montreal. The Expos released him two months later.