Pelluer attended Interlake High School in Bellevue, Washington, a suburb east of Seattle, and lettered in football and basketball.
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.
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 (which included a third-and-15 conversion) for the winning touchdown, leading the Cowboys to a victory that clinched the division title.
When White suffered a season-ending injury (broken wrist) in week 9 against the New York Giants, Pelluer nearly rallied the team after completing 28-of-38 passes for 339 yards.
In 1989, he asked to be traded, after Jimmy Johnson was hired as the new head coach and drafted two rookie quarterbacks (Troy Aikman and Steve Walsh).
On November 5, he led his team to a 20–10 win against the Seattle Seahawks and tied a franchise record for rushing yards (69) by a quarterback.
In 1996, he played with the Frankfurt Galaxy of the World League of American Football, reuniting with head coach Ernie Stautner, who was the defensive coordinator with the Dallas Cowboys.
Pelluer's late brother, Scott, attended Washington State University and played linebacker for the New Orleans Saints.