Kramer played his high school football at Robert E. Lee High School in San Antonio. He guided the Volunteers to a state title in 1971 and then to the state semi-finals in 1972. The state championship game in 1971 was the first high school game played in the new Texas Stadium (Dallas Cowboys) in Irving, Texas. Kramer guided the Lee Volunteers to a 28–27 victory which has been hailed by some as the best high school game ever played in Texas. Kramer's high school teammates included Pat Rockett (played major league baseball for the Atlanta Braves), and Richard Osborne (played for the NFL's Philadelphia Eagles).
The Volunteers went 27–1–1 during Kramer's two years on the varsity, beating Wichita Falls High School 28–27 for the Class 4A state title in 1971 and losing to Baytown Sterling 21–20 in the 1972 state semifinals. Guided by head coach John Ferrara, the 1971 team finished 14–0–1 – a 7–7 tie with rival Churchill kept the Volunteers from being perfect – and the 1972 squad went 13–1. In an era when most Texas high school football teams churned out yardage with ground-oriented offenses such as the wishbone or the veer, Lee achieved success by throwing the ball.
Kramer passed for 2,588 yards as a senior, then a state record, and completed 149 of 294 passes for 28 touchdowns. In two seasons, he completed 327 of 597 attempts for 5,489 yards and 54 TDs. Surrounded by sure-handed receivers Richard Osborne, Pat Rockett and Gary Haack, Kramer was a master at picking apart defenses with his deft passing. Kramer started all but one game as a varsity player, going 26–1–1. He made his debut in the 1971 season opener, replacing starter Bruce Trimmier and rallying Lee to a 7–3 victory over Alamo Heights on a rainy night.
After a stellar career at Lee, Kramer became another in the long list of San Antonio products to play college football at Rice University.
Kramer led the Owls in passing for four straight years and his career and season marks were the standard at Rice for over 30 years until they were shattered by Chase Clement, another San Antonio signal caller. Kramer left Rice with school records in single-season passing yards, career passing yards (6,197); season total offense (3,272), career total offense (6,336), season touchdown passes (21), career touchdown passes (37), season total touchdowns (25) and career total touchdowns (48). He was the 1976 George Martin Award winner as Rice's MVP in 1976 and was elected to the Rice Athletic Hall of Fame in 1984.
Kramer played in the Senior Bowl and the Blue-Gray Game in 1976 and was named MVP of the Senior Bowl. He also received the Fort Worth Kiwanis Sportsmanship Award in 1976.
Kramer became the starting quarterback for the Vikings before the 1979 NFL season, when Fran Tarkenton retired. The Vikings drafted him as Tarkenton's heir apparent. He earned the nickname "Two-Minute Tommy" for his many late-game come-from-behind victories, including in the final home game of the 1980 season, against the Cleveland Browns, in which he threw a game-winning Hail Mary pass with six seconds left. Ahmad Rashād was clustered in a group of Browns defenders but managed to catch the ball and back into the end zone. The play became known as the Miracle at the Met, and although they lost their final game the next week, the Vikings made the playoffs at 9–7.
Throughout his career with the Vikings, Kramer suffered on-the-field injuries, resulting in many missed games during the mid-1980s. He was selected for the Pro Bowl following the 1986 season, in which he was the NFL's highest-rated quarterback. Kramer was the first NFL quarterback to throw for over 450 yards in a game twice, and once threw six touchdowns in a single game, versus the Green Bay Packers. He was released by the Vikings after the 1989 season and signed by the New Orleans Saints in 1990. He appeared in only one game for the Saints (against the Vikings) and retired after the 1990 season.