Pelluer attended Interlake High School in Bellevue, Washington, a suburb east of Seattle, and lettered in football and basketball. In football, he led his team to the state quarterfinals in his last two years. As a senior, he received All-state honors and was a National Football Foundation Scholar-Athlete. Pelluer's family had a tradition of playing football at Washington State University in Pullman, but he accepted a scholarship from the rival University of Washington in Seattle. As a sophomore in 1981 under head coach Don James, Pelluer took over the starting quarterback position, after Tim Cowan injured his thumb in the second game of the season. He finished with 110 of 234 completions, for 1,138 yards and 9 touchdowns, while leading the team to a Pacific-10 Conference title and a 28–0 win over the University of Iowa in the Rose Bowl on New Year's Day. Even though his record was 7–1, Pelluer lost the starting job to Cowan in 1982. In his senior season in 1983, he had one of the best quarterback seasons in school history, receiving All-Pac-10 and the conference's offensive player of the year honors, after completing a 67.2% of his passes for 2,365 yards and 11 touchdowns. He also set a school record with most consecutive passes completed without an interception. Pelluer left as the school's second career leader in passing yards with 4,603 passing yards, to go along with 436 completions, 30 touchdowns, 342 rushing yards and a record.
Professional career
Dallas Cowboys
Pelluer was selected by the Dallas Cowboys in the fifth round of the 1984 NFL Draft. He also was selected by the Oakland Invaders in the sixth round of the 1984 USFL Draft. He was the third-string quarterback in his first two years. In 1985, with the first place in the NFC East division at stake, he was forced to enter a close game against the New York Giants and make his career debut, because both starting quarterback Danny White and backup Gary Hogeboom had been injured. Pelluer on his second series directed a 72-yard drive for the winning touchdown, leading the Cowboys to a victory that clinched the division title. In 1986, he was named the backup quarterback after Hogeboom was traded. When White suffered a season-ending injury in week 9 against the New York Giants, Pelluer nearly rallied the team after completing 28-of-38 passes for 339 yards. He started 6 out of the last 7 games, showing a strong arm and great mobility. Against the Seattle Seahawks, he set the franchise record for consecutive passes completed without an incompletion. He finished with a 1–6 record and was sacked 47 times in 9 starts. In 1987, he began as a backup, but took over White in week 10 against the Miami Dolphins and started 4 out of the last 6 games. He finished with 94 straight passes without throwing an interception. In 1988, at a low point in franchise history, he started 14 of the 16 games, passing for 3,139 yards, 17 touchdowns, rushing for 314 yards and 2 touchdowns, but the team finished just 3–13. In the seventh game against the Chicago Bears, while sliding feet first, a fierce hit by linebackerMike Singletary forced him to leave the game with a concussion.. In the eighth game against the Philadelphia Eagles, he completed 32 out of 46 passes for 342 yards. In the fifteenth game against the Washington Redskins, he passed for 333 yards and 3 touchdowns. He was the last quarterback to start and win a game for a Tom Landry-coached team and became one of only 3 quarterbacks in franchise history to pass for more than 3,000 yards in a season, joining Roger Staubach and Danny White. The next year, he asked to be traded, after Jimmy Johnson was hired as the new head coach and drafted two rookie quarterbacks. On October 17, 1989, he was traded to the Kansas City Chiefs in exchange for a third round draft choice in 1990 and a fourth round draft choice in 1991.
Kansas City Chiefs
In 1989, he appeared in 5 regular season games with 3 starts. On November 5, he led his team to a 20–10 win against the Seattle Seahawks and tied a franchise record for rushing yards by a quarterback. In 1990, he appeared in 13 games with no starts, after Steve DeBerg established himself as the team starter during the preseason. On August 7, 1991, he walked out of training camp, before returning on August 19. He was released on August 27 and later re-signed on December 17 to back up Mark Vlasic after DeBerg was injured.
In 1995, Pelluer signed with the Winnipeg Blue Bombers of the Canadian Football League after being out of football for three years. He was lost for the season after dislocating his shoulder in the second game against the Birmingham Barracudas.