Biffle traveled around the 1.5-mile Texas Motor Speedway at 193.736 mph for his third pole of the season and the ninth of his Sprint Cup career. He won on this track in 2005.
His lap time was .001 of a second faster than Roush Fenway Racing teammate David Ragan.
Matt Kenseth, another Roush driver, qualified third -- the best showing among the drivers who are part of the Sprint Cup chase for the championship.
Edwards leads Stewart by eight points in the championship chase with three races remaining in the Sprint Cup season. Kevin Harvick, who is third in the chase, qualified 21st.
The 500-mile race is scheduled to be run Sunday, although there is a chance of rain in the forecast.
Megyn Kelly: Santa Claus and Jesus are both white men
Costly malfunction causes beer flood at Boston-area brewery