Garrett originally played college football at Princeton University, but transferred to Columbia University when his father, Jim Garrett, became the head coach. Following his father's resignation as head coach after Columbia's 0–10 1985 season, Jason and his brothers, John and Judd, transferred back to Princeton. At Princeton in 1987 and 1988, Garrett completed 366 of 550 passes (66.5%) for 4,274 yards and 20 touchdowns and won the Asa S. Bushnell Cup as the Ivy League Player of the Year. In 1988 he piloted Princeton in a losing effort against his former team, snapping Columbia's 44-game losing streak. He earned a degree in history in 1989. He continues to hold the Ivy League career record for completion percentage with 66.5% (366–550) and his 1988 percentage of 68.2% (204–299) stood as the league record until 2000, when Gavin Hoffman posted a 70.5% mark.
He signed as a free agent with the New Orleans Saints in 1989. In 1991, Garrett started at quarterback for the San Antonio Riders of the World League of American Football, but suffered a separated shoulder in the season opener. He'd return to play for the Riders later in the season, but was supplanted by Mike Johnson in the lineup. In 1991, Garrett played for the Ottawa Rough Riders of the Canadian Football League. In 1993, Garrett went to the Dallas Cowboys, where he was the third-string backup to Troy Aikman on the 1993 and 1995 Super Bowl winning teams. In eight seasons with the Cowboys, Garrett played in 39 games and completed 165 of 294 passes (56.1%) for 2,042 yards, 11 touchdowns, and 5 interceptions. The highlight of his career with the Cowboys occurred on the 1994 Thanksgiving Day game when Garrett, starting in place of injured back-up Rodney Peete, led the Cowboys over the Green Bay Packers by completing 15 of 26 passes for 311 yards and 2 touchdowns in a second-half comeback. In 2008, that game was named the fourth-best moment in the history of Texas Stadium by ESPN. Garrett was promoted to second string Cowboys quarterback for the 1998 and 1999 seasons. Garrett started 5 games in 1998 while Aikman was injured (leading the team to a 3–2 record) and started two in 1999 (going 1–1). In 2000, he went to the New York Giants, where he appeared sparingly as the backup to Kerry Collins from 2000 to 2003. In 2004, after a short stint as a backup with the Tampa Bay Buccaneers, he went to the Miami Dolphins.
In January 2007, Garrett was hired by the Dallas Cowboys as offensive coordinator. He guided the Cowboys to the 2nd best offense in the NFL, which made him an attractive head coaching prospect. In January 2008, Garrett interviewed for the head coaching job of the Baltimore Ravens and the Atlanta Falcons receiving offers from both, but ultimately opted to remain in Dallas. His salary for the 2008 season was nearly $3 million; the highest salary for an assistant coach in the NFL at the time. On December 29, 2008 the Detroit Lions received permission to speak to Garrett regarding the team's head coaching vacancy according to ESPN sources. In January 2009, the Denver Broncos also interviewed him as a possible replacement for fired coach Mike Shanahan. He was also a finalist for the St. Louis Rams head coaching position, to replace Jim Haslett, the interim head coach. Ultimately, he lost the job to Steve Spagnuolo.
On November 8, 2010, he was named as the Dallas Cowboys' interim head coach following the firing of Wade Phillips after the Cowboys' 1–7 start for the 2010 season. On November 14, 2010, Garrett won his first game as a head coach, beating the favored New York Giants 33–20 in the Meadowlands. The next week, he led the Cowboys to a 35–19 victory over the Detroit Lions, their first home win all season. On January 6, 2011, Garrett was named the official Cowboys head coach; the 8th in Cowboys history, and the first born during the team's era.
The 2014 season saw Garrett achieve bona fide head coaching success for the first time. His Cowboys, featuring several key draft picks maturing as top-level offensive lineman and the emergence of DeMarco Murray as a dominant running back, won the NFC East with a 12-4 record and were tied for the best record in the conference with the Green Bay Packers and the Seattle Seahawks. The Cowboys were undefeated on the road, including impressive wins over Seattle and the arch-rival Philadelphia Eagles. Garrett's team lost the three-way tiebreaker to Green Bay and Seattle and therefore hosted the Detroit Lions in the Wildcard game. This game, won 24-20 by the Cowboys, featured a controversial "flag pick up" after a penalty during a late Detroit drive thereby allowing Dallas an improved chance to make a comeback and defeat the Lions. In the ensuing Divisional Playoff, hyped as a rematch of the famous Ice Bowl NFL championship game from 1967, Dallas held a lead in the second half, but, after losing the lead due to a late Aaron Rodgers touchdown pass, had a potentially game winning catch by Dez Bryant overturned in official replay, therefore sealing a 26-21 defeat to Green Bay. On January 13, 2015, Jerry Jones and Garrett came down to an agreement of a contract, keeping him in Dallas for 5 more years, while getting paid $30 million.
Jason's brothers, John and Judd, also played in the WLAF, and Judd made second-team All-World League in 1991 after leading the league in catches. John is currently wide receivers coach for the Tampa Bay Buccaneers, and his younger brother, Judd, works in the Dallas Cowboys front office after being let go as tight ends coach for the St. Louis Rams. Since he played for the London Monarchs, Judd is the only one of the Garretts who played in the WLAF to have a World Bowl ring. Another brother, Jim Garrett III, is an English teacher and former football coach at University School in Hunting Valley, Ohio.