Dallas Drake began his trek to the NHL playing Junior A hockey for the Vernon Lakers of the BCJHL in 1987-88 at the age of 18. In 47 games, he scored 124 points and in the playoffs, notched 26 points in eleven games. In 1988-89, he enrolled at North Michigan University and scored 39 points as a WCHA freshman and guided the school to a WCHA championship. After scoring 37 points as a sophomore in 1989-90, Drake improved to 22 goals and 58 points in 1990-91. He was a key factor in the team winning the 1991 NCAA championship final by scoring the winning goal in triple overtime. In 1991-92, he led the WCHA with 39 goals and 80 points. That year, he was a WCHA First Team All-Star, an NCAA West First Team All-American and winner of the WCHA Player of the Year award. In 1993-94, Drake played one game on a conditioning stint with the AHL's Adirondack Red Wings.
Drake was selected 116th overall in the 1989 NHL Entry Draft by the Detroit Red Wings. He made his NHL debut on October 6, 1992 against the Winnipeg Jets and scored his first goal two weeks later on October 20 against those same Jets. That rookie season, Drake contributed 18 goals and 44 points in 72 games. In 1993-94, he was traded to the Winnipeg Jets. In 62 games split between the two teams, he scored 13 goals and 40 points before establishing a career-high 19 goals in 69 games in 1995-96. In 1996-97, Drake moved with the franchise to Phoenix and in 1999-00, he played 79 games and scored a career-high 30 assists and 45 points and had five game-winning goals. On June 23, 2000, Drake's rights were selected in the Expansion Draft by the Columbus Blue Jackets. On July 1, however, he signed as an unrestricted free agent with the St. Louis Blues and has been a key role player for the past four seasons.