Brazzell attended Alice High School, where he helped start a run by the Coyotes as a playoff powerhouse through the 1990s.
Brazzell was selected by the New York Jets in the sixth round (174th overall) of the 1998 NFL draft, because they coveted his track speed.
Because of injuries to the receiving corps, he was promoted to the active roster in week 14 and registered his first reception in a 20–10 win against the Philadelphia Eagles, a 12-yard catch from quarterback Troy Aikman.
[5] On October 15, Brazzell was signed to the practice roster of the Edmonton Eskimos in the Canadian Football League.
Brazzell played in 11 games in his second season, finishing fourth among Edmonton wide receivers with 30 receptions for 546 yards and three touchdowns.
One of his personal highlights was a 101-yard reception for a touchdown from Jason Maas in a 27–21 season-opening win against the Calgary Stampeders.
He continued to make big plays in the post-season, registering 4 receptions for 79 yards in a 33-30 Western Final against Winnipeg.
He had perhaps his best game of the season in the Lions' 26–20 victory on September 20 against the Winnipeg Blue Bombers when seven receptions for 157 yards.
He had the first multi-to game of his CFL career when he hauled in a pair of scores in the Lions' August 22 victory against the Hamilton Tiger-Cats.
In 2004 Brazzell finished fourth on the BC Lions in receiving with 49 receptions for 906 yards and eight touchdowns in 16 games.
He also had a pair of passes in the Leo's 27–19 loss to the Toronto Argonauts in that year's Grey Cup championship.
On August 9, 2005, Brazzell was traded to the Winnipeg Blue Bombers in exchange for Canadian receiver Kamau Peterson.
Although Brazzell was scheduled to become a free agent on February 16, 2007, he chose to re-sign with the Blue Bombers.