In 1938, O’Brien threw for 1,457 passing yards — a Southwest Conference record that stood for ten years. He had only four interceptions in 194 passing attempts, and his NCAA record for most rushing and passing plays in a single season still stands today. That season, he led the Horned Frogs to an undefeated season, as they outscored their opponents by a 269-60 margin and held nine of their ten regular-season opponents to seven points or less, including three shutouts. They finished the season with a 15–7 victory over Carnegie Tech in the 1939 Sugar Bowl and the National Championship title. O’Brien was named to 13 All-America teams and became the first player to win the Heisman, Maxwell and Walter Camp trophies in the same year. He was also the first Heisman winner from TCU and the first from the Southwest Conference. He was also a member of the Texas Gamma chapter of Sigma Phi Epsilon fraternity.
O'Brien was drafted in the first round (fourth overall) of the 1939 NFL Draft by the Philadelphia Eagles, who gave him a $12,000 bonus and a two-year contract. In his first season in the NFL, he led the NFL in passing yards as a rookie with 1,324 yards in 11 games, breaking his old TCU teammate Sammy Baugh's single season passing yardage record. In 1940 he again led the league in several passing categories, including attempts and completions. The Eagles gave him a $2,000 raise, but he retired after the 1940 season.
In his professional career, O'Brien completed 223 of 478 passes for 2,614 yards and 11 touchdowns. He was also a defensive back and punter, intercepted four passes for 92 yards and punted nine times for an average of 40.7 yards per kick.