Thurman accepted a football scholarship from the University of Southern California. As a freshman, he was part of the 1974 National Champion team. He played for John McKay and later for John Robinson. He started 5 games at flanker in his first two seasons, recording 3 receptions for 55 yards and 7 carries for 61 yards. As a junior in 1976, he was named the starter at free safety, leading the team and the Pacific-8 Conference with 8 interceptions. He intercepted passes in seven straight contests. He led the nation with in interception return yardage. He also led the team with 17 punts for 68 yards. As a senior in 1977, he was second on the team with 3 interceptions. He was named the team's MVP and its Defensive Player of the Year. He played in the 1978 Senior Bowl and was a Playboy Pre-Season All-American. Thurman is tied for sixth in school history with 13 interceptions, 2 of which were returned for touchdowns. He also had 77 tackles, 6 pass deflections and 7 fumble recoveries. He played on Trojan teams that won four bowl games. Teammate Ronnie Lott credits Thurman for his development as a player in his Pro Football Hall of Fame speech stating Thurman was someone who "helped me become a better football player."
Thurman was selected by the Dallas Cowboys in the 11th round of the 1978 NFL Draft, after dropping because he was considered too small and slow to play professional football. Although his college experience was at safety, he made the team as a backup cornerback. As a rookie, he also played on special teams, recovering an onside kick in Super Bowl XIII. He finished the season with 20 tackles and 2 interceptions. In 1979, he regularly replaced outside linebacker D. D. Lewis on passing situations. He also played strong safety in place of an injured Randy Hughes. He started at cornerback in the season finale against the Washington Redskins. He had 37 tackles, one fumble recovery, one interception in the regular season and one in the divisional playoff game against the Los Angeles Rams. In 1980, he started at free safety in place of an injured Hughes. In the ninth game against the St. Louis Cardinals, he returned an interception for a 78-yard touchdown. Although his play was inconsistent, he still tied Charlie Waters for the team lead with 5 interceptions. He also had 101 tackles, 2 forced fumbles and 2 fumble recoveries. In 1981, after Charlie Waters retired, cornerback Benny Barnes was moved to strong safety and rookie Michael Downs to free safety, so Thurman became the starter at right cornerback. He registered 76 tackles, one fumble recovery and 9 interceptions, which was second on the team to Everson Walls' 11 picks. In the season opener against the Washington Redskins, he returned an interception 96 yards for a touchdown, which was the second longest in club history. He had 2 interceptions in the 28–27 win against the Miami Dolphins. In the fifteenth game against the Philadelphia Eagles, he tied a franchise record with 3 interceptions in a single-game, helping to clinch the NFC East championship. His 187 interception return yardage in the season ranked second in club history. He had 2 interceptions in the 38-0 playoff win against the Tampa Bay Buccaneers. In 1982, he made 43 tackles and 3 interceptions. He returned a 60-yard interception for a touchdowninterception against the Minnesota Vikings. He tied a club and an NFC playoff record with 3 interceptions, including a 39-yard return for touchdown to clinch a victory in the playoffs second round against the Green Bay Packers. In 1983, he collected 66 tackles, one fumble recovery and led the team with 6 interceptions. He scored his fourth career touchdown when he recovered a fumble against the St. Louis Cardinals. In 1984, he was moved to backup Downs at free safety and was more involved in third-down defensive schemes. He registered 34 tackles and 5 interceptions. During the 1985 season quarterback Danny White nicknamed Thurman along with fellow safety Michael Downs and cornerbacks Walls, Ron Fellows, "Thurman's Thieves", for their opportunistic play in the secondary, as they combined for 33 total interceptions. He posted 41 tackles and 5 interceptions. He returned an interception 21 yards for a touchdown in the season opener against the Washington Redskins, contributing to a 44–14 win. He had 2 interceptions against the Cleveland Browns, that stopped 2 scoring opportunities in a 20–7 win. Thurman was waived on August 26, 1986. He left with a franchise record of career 4 interceptions returned for touchdowns, he ranked fourth in regular season career interceptions, second in playoff interceptions and third in interception return yardage. At the time, he also ranked third in league history for career playoff interceptions.
St. Louis Cardinals
On August 28, 1986, he was claimed off waivers by the St. Louis Cardinals, reuniting with head coach Gene Stallings who was his defensive secondary coach with the Cowboys. He played safety and started three games. He was released on December 22. Thurman never missed a game during his 137-game career and finished with 36 interceptions, which he returned for 562 yards and four touchdowns, while also recovering seven fumbles.
Thurman was named defensive backs coach upon the hiring of Rex Ryan as head coach of the Jets. During his tenure, he coached Darrelle Revis and Antonio Cromartie. Revis and Cromartie were vital parts of the Jets defense, especially during the Jets' playoff appearances in 2009 and 2010. Under Thurman's coaching, Revis was described as "one of the best" corners in the league. After five seasons, Thurman was promoted to defensive coordinator after the 2012 season.
Defensive coordinator (2013–2014)
Thurman was named Defensive Coordinator prior to the 2013 season. In his first season, the Jets defense allowed 24.2 points per game against. Thurman's defense was sixth in the league in his final season in New York, allowing 327.2 yards per game. They also finished in the top five among defenses against the running game. Following the 2014 season, he joined Rex Ryan's coaching staff for the Buffalo Bills.
Buffalo Bills (2015–2016)
On January 15, 2015, Thurman was hired by new head coach Rex Ryan to serve as the defensive coordinator. Thurman was credited for helping cornerback Stephon Gilmore emerge. The Bills ranked 19th in the league in defense in his first season and 14th in 2016. He was fired on January 14, 2017.
Memphis Express (2018)
In October 2018, Thurman was named defensive coordinator for the Memphis Express of the Alliance of American Football.
