He played college football for the Tulane Green Wave and Northeast Louisiana Indians before being selected in the third round of the 1986 NFL draft by the Steelers.
Over the years Pittsburgh sports writers and Steelers fans frequently made jokes about Brister's thick Southern accent and perceived lack of sophistication, traits of Bradshaw's that were similarly mocked.
Career highlights during his 1988–1991 run as Pittsburgh's starting quarterback included ranking fourth in the NFL in average yards per pass completion in 1988 and 10th in the league in passer rating in 1990.
In 1989, he set a team record with 15 consecutive pass completions in a road win over Detroit, including a 48 yarder to Lipps.
Brister was the starting quarterback during Hall Of Fame Coach Chuck Noll's final post season run with the Steelers, winning the 1989 AFC Wild Card in overtime on the road against the Houston Oilers, then losing a close game to eventual AFC champion Denver Broncos.
Even though Brister was not forced to enter that late-season loss against Houston, he did supplant the struggling O'Donnell the next week, starting the team's final two games, both wins over Cincinnati and Cleveland.
In two other games Brister came off the bench, relieving a struggling O'Donnell after he was hurt and leading fourth-quarter comebacks over the Seattle Seahawks and Detroit Lions.
In his first season in Philadelphia in 1993, Brister ranked seventh in the league in passer rating and fourth in lowest interception percentage, starting 8 games with two relief appearances subbing for an injured Randall Cunningham.
Highlights of the season included his 27 completions, 245 yards, two touchdowns performance vs. the Super Bowl champion Dallas Cowboys on Monday Night Football, and his 353 yards, three touchdowns performance in the final game of the regular season, again on Monday Night Football, leading the Eagles to a win over NFC West champion San Francisco.
Brister's interception percentage that year was the lowest in Eagles team history for more than a decade until eclipsed by Donovan McNabb.
However, when Elway retired in 1999, Brister was passed over for the starting spot in favor of Brian Griese, and the Broncos released him after that season.