Phipps attended Purdue University, where he played for the Purdue Boilermakers football team. He began his college career when he replaced All-American Boilermakers quarterback Bob Griese. His first major victory was a 28-21 upset of defending national champion Notre Dame Fighting Irish on September 30, 1967. Combining strong passing skills with excellent mobility helped Phipps establish a new school single-season record for total offense and earn the Boilermakers a share of the Big Ten Conference title.
The following year, Phipps suffered an ankle injury that kept him out of two games, and was overshadowed by teammate Leroy Keyes, a running back who spent all season in contention for the Heisman Trophy. The Boilermakers were the top-ranked team in the country until the Ohio State Buckeyes upset them 13-0 on October 12.
In 1969, Phipps became the focal point of Purdue's offense, throwing for five touchdowns in a 36-35 thriller over Stanford University on October 4, including throwing for a two-point conversion with three minutes left. He also defeated Notre Dame for the third consecutive year. Phipps finished second in the voting for the Heisman Trophy to Oklahoma Sooners running back Steve Owens.
Although he was awarded the 1969 Sammy Baugh Trophy, he declined a Rhodes Scholarship to concentrate on a professional football career.
Phipps was picked third in the 1970 NFL Draft by the Miami Dolphins, who traded him to the Cleveland Browns for All Pro wide receiver Paul Warfield on January 27, 1970. Phipps saw limited action during his first two seasons. In the team's third game of the 1970 NFL season, Phipps came off the bench to lead a 15-7 comeback victory over the Pittsburgh Steelers. However, his lone start of the year would be a 14-10 loss to the Cincinnati Bengals on November 15, 1970, as the rookie finished with 529 passing yards on the season. The following year, Phipps threw for only 179 yards and started just one contest: a 13-7 defeat to the Kansas City Chiefs on November 14.
In 1972, Phipps again began the season on the sidelines, but became the team's starting quarterback after a disappointing 26-10 opening game loss to the Green Bay Packers on September 17. He threw for 13 touchdowns and nearly 2,000 yards, helping the Browns reach the NFL playoffs. In the November 13 game against the San Diego Chargers, he led a last-minute drive to win the 21-17 contest. In the team's playoff clash against the undefeated Miami Dolphins on December 24, Phipps had led the team to a 14-13 fourth quarter lead, but his five interceptions helped end hopes of a possible upset.
The following year, he threw for nine touchdowns, but was intercepted 20 times. Despite these struggles, he engineered two late-season comebacks in a win over the Steelers and a tie against the Kansas City Chiefs. However, the Browns missed the playoffs with a 7-5-2 record. In 1974, the team collapsed with a 4-10 record, and Phipps was briefly replaced by Brian Sipe at mid-season.
The 1975 season was even more disastrous as the Browns dropped their first nine games. However, Phipps went 23 of 36 in the team's first victory, a 35-23 win over the Cincinnati Bengals on November 23 in Cleveland. Phipps threw for a personal high of 298 yards with 2 TD passes and no interceptions. Two other victories helped give hope for a turnaround the following season.
In the team's 1976 opener against the New York Jets, Phipps started the game, but suffered a separated shoulder after being tackled by the Jets' Shafer Suggs. By the time he had recovered from the injury, Sipe had established himself as the team's new leader and Phipps' time in Cleveland was soon to come to an end.
That finish came on May 3, 1977, when Phipps was traded to the Bears for a first round draft pick in 1978, which turned out to be Hall of Fame tight end Ozzie Newsome. He saw minimal action during the 1977 NFL season, threw for two touchdowns (along with 10 interceptions) the next year, but saw his most extensive action in 1979. During that year, he threw for 1,535 yards and nine touchdowns, as he battled teammates Bob Avellini and Vince Evans for playing time.
Phipps threw for a pair of touchdowns in each of the next two seasons, but his limited role and the arrival of both quarterback Jim McMahon in the 1982 NFL draft and new coach Mike Ditka resulted in his release.