Dawson attended Lake Highlands High School in Dallas, Texas and was a letterman in football. In a 1992 playoff game at Texas Stadium against Nacogdoches High School, Dawson kicked a 52-yard field goal as time expired to beat Nacogdoches 31-28. He graduated in the class of 1993; the Baltimore Ravens placekicker Matt Stover attended the same high school, graduating in 1986. As a senior, he was a starter at both kicker and offensive tackle until he hurt his knee in a preseason scrimmage. He thought he might have to have season-ending surgery, but he gutted it out, stuck to kicking, and was named as an All-American and the Southwest Region Offensive Player of the Year by SuperPrep.

The Cleveland Browns signed him as a free agent in March 1999, and he remained with the team for 14 years until he joined the San Francisco 49ers in 2013. (He was the only player left from the 1999 Browns squad). Dawson holds the Browns record for most consecutive field goals made (29) and most field goals in a game (6). Dawson is currently the 7th most accurate kicker in the NFL. On October 10, 2010, Dawson tied Lou Groza for the Browns’ career field-goal record with 234.

Dawson scored the first points in the history of the “new” Cleveland Browns in 1999. On October 10 of that year, he scored the only touchdown of his career on a fake field goal against the Bengals in an 18-17 loss.

Dawson had a rule named after him after a missed call by referees. On November 18, 2007, Dawson attempted a 51-yard field goal in the closing seconds of the fourth quarter to tie the game against the Baltimore Ravens. The kick carried through the air and hit the left upright and then the rear curved support post (stanchion), which bounced the football over the crossbar and into the end zone, in front of the goalpost. The kick was originally ruled no good. Under NFL rules, the play was not reviewable. Officials discussed the play among themselves for several minutes and decided that, since the ball had indeed crossed the crossbar within the goal, whatever happened afterward to the ball did not matter. The kick was considered good, as announced by referee Pete Morelli. However, as the play is not technically reviewable, referee Pete Morelli announced that the play was reversed “after discussion,” as opposed to “after further review,” as is usually stated. At this point the Ravens, already celebrating in the locker room (they would have won 30-27 if the field goal was no good), were called back out onto the field to proceed to an overtime period. The Browns went on to win the game, 33-30 in overtime, as Dawson came through again with a more visible 33-yard field goal. Dawson finished 4 for 5 in FGs whereas fellow Lake Highlands High School alumnus Matt Stover finished 3 for 3 in FGs for the Ravens.

On November 17, 2008, Dawson hit a 56-yard field game-winning field goal against the Buffalo Bills on Monday Night Football.

Dawson signed with the San Francisco 49ers on March 19, 2013. He made a career best 27 consecutive field goals during the 2013 season, until the streak was snapped by a 24-yard field goal miss against the Arizona Cardinals in Week 17. He finished his first year in San Francisco with the second-most points (140) and field goals (32-of-36) in the team’s history. Dawson kicked the game-winning field goal in the 49ers Wild Card playoff game against the Green Bay Packers on January 5, 2014, giving the 49ers a 23-20 victory.

On September 26, 2013, Dawson attempted and missed a 71-yard fair catch kick in the last seconds of the second quarter of a game against the St. Louis Rams.

Dawson resides in Austin, Texas with his wife, Shannon, and 3 kids, Dru, Beau, and Sophiann. As of 2018, Dru is the starting varsity QB at Vandegrift High School as a junior while other son Beau is also on the varsity as a freshman backup. Dawson kicks right-footed but throws left-handed. His wife Shannon is a singer-songwriter and produced her first album “Redemption” in 2013.

On March 11, 2014, Dawson signed a new two-year contract to remain with the 49ers.

Dawson re-signed with the 49ers on a one-year contract on March 12, 2016. He made his 400th career field goal on November 20, 2016 against the Patriots.

On March 10, 2017, Dawson signed a two-year contract with the Arizona Cardinals.

On September 10, 2017, in the season opening 35–23 loss to the Detroit Lions, Dawson made his debut as a Cardinal. He converted two extra points and a field goal in the loss.

On September 17, 2017, Dawson converted three field goals, including a 40-yarder to force overtime and a 30-yarder in overtime to win, in the 16–13 victory over the Indianapolis Colts.

On November 26, 2017, Dawson hit a 57-yard field goal with one second left to beat the favored Jacksonville Jaguars. It was the longest made field goal of Dawson’s career (although he made a 59-yard field goal during a 2010 preseason game with the Browns). He converted four field goals in the game, including the 57-yard game-winner, earning him NFC Special Teams Player of the Week.

On November 26, 2018, Dawson was placed on injured reserve with a hip injury.

Dawson announced his retirement after 21 seasons on August 1, 2019, after signing a one-day ceremonial contract with the Browns to retire as a member of the team. After Dawson’s retirement, Adam Vinatieri became the sole remaining active player from the 1990s.

On March 6, 2020, Dawson was named Special Teams Coordinator at Lipscomb Academy in Nashville, TN.