Jefferson played at Arizona State University from 1974 to 1977. Jefferson's breakout year occurred in his sophomore season (1975) when he led the Sun Devils with 52 receptions and 921 yards receiving on the way to a perfect 12-0 season and an appearance in the Fiesta Bowl, where he was also named Most Valuable Player. ASU finished second in the national polls, its highest ranking in history.
A consensus All-American selection in 1977 and two-time All-Western Athletic Conference pick, Jefferson concluded his career with an NCAA record 42 consecutive games with a reception. He remains the ASU leader in career receptions with 188 and career receiving yardage with 2,993. Recognized as Arizona Amateur Athlete of the Year in 1977, he was twice selected as the Sun Devils Most Valuable Player and led the team in receiving all four years. The 1977 campaign was the Sun Devils' last in the WAC; in 1978, ASU and their in-state archrival, the Arizona Wildcats, joined the Pacific-10 Conference.
After his senior year at Arizona State, Jefferson was drafted fourteenth overall in the 1978 NFL Draft by the San Diego Chargers. Jefferson made an immediate impact in the NFL, finishing his rookie season with 56 receptions for 1,001 yards and a league-leading 13 receiving touchdowns, which tied the NFL record for most receiving touchdowns by a rookie. He set the Chargers' rookie record for yards receiving, which stood until Keenan Allen's 1,046 in 2013. Jefferson appeared on the cover of the August 20, 1979 issue of Sports Illustrated along with the heading "The Touchdown Man." He was a consensus All-Pro in each of the next two seasons and led the NFL in receiving yards (1,340) and receiving touchdowns (13) in 1980. In a September 14, 1980, overtime game against the Oakland Raiders, played in San Diego, Jefferson out-leaped Lester Hayes for a throw from Dan Fouts. Jefferson landed at about the Oakland 3-yard line. Hayes stood over Jefferson, stunned that Jefferson had taken the ball away while Jefferson rolled untouched into the end zone, sealing a 30-24 San Diego Chargers' overtime victory. He became the first receiver in league history to gain 1,000 yards in each of his first three seasons. While in San Diego, Jefferson also became known as the "Space-Age Receiver" due to the futuristic-looking goggles he wore. With his acrobatic catches and fiery enthusiasm before games, he became a fan favorite in San Diego. Jefferson caught a pass in 44 of his 45 regular season starts with San Diego. He did not catch a pass on September 16, 1979, against the Buffalo Bills, who double-teamed him. The Chargers did not target him on any pass plays, but the attention he drew instead helped the team rush for 245 yards.
Due to a contract dispute with the Chargers, Jefferson was traded to the Green Bay Packers in 1981. With the Packers, Jefferson starred opposite future Pro Football Hall of Fame wideout James Lofton. Jefferson, Lofton, and tight end Paul Coffman teamed up with quarterback Lynn Dickey to give the Packers one of the most explosive passing attacks in the NFL at the time; however, a defense which hovered near the bottom of the league relegated Green Bay to three 8-8 finishes and a second-round playoff appearance during the strike-shortened 1982 season. Jefferson completed his career with the Cleveland Browns in 1985. Jefferson would appear in four Pro Bowls during his career. He, along with Charlie Joiner, Kellen Winslow and Wes Chandler (who replaced him on the Chargers) represented one of the most potent receiving corps of the early 1980s, known as Air Coryell. Jefferson was known for making spectacular catches with his body control and great hands.
He has remained active in the football community; after retiring, Jefferson became an assistant coach at the University of Kansas and was the director of player development for the Washington Redskins until the end of the 2008–2009 season.