Biffle, who was quickest in practice earlier in the day, turned a lap at 193.736 mph around the fast 1.5-mile track for his third pole of the season and the ninth of his Sprint Cup Series career. He won the spring 2005 race at Texas.
"Being a former winner here and running good at this racetrack, that gives me a lot of confidence going into this weekend," Biffle said. "The car was really fast right off the track."
Biffle's lap, the fastest in all of the Sprint Cup qualifying sessions so far this year, was only 0.001 seconds quicker than Ragan's lap.
"I didn't really think we would have a shot at the pole going into qualifying," Ragan said. "That was close. I told Greg that he just barely beat me. That's cool to be that fast in qualifying."
Biffle and Ragan are not in this year's Chase for the Sprint Cup championship field.
Matt Kenseth, also from Roush Fenway, was the highest finishing Chase driver in qualifying with a third-place showing. Kenseth won here in April.
With three races to go, Edwards holds just an eight-point advantage over Stewart. Edwards has the most victories at Texas with three.
"We wanted to be a little bit better than that," Edwards said after his seventh-place finish in qualifying. "It is a good starting spot. We focused hard on qualifying here. We had an opportunity to go out there and sit on the pole. And now we just work on the race trim."
Kevin Harvick, who is 21 points behind Edwards, qualified 21st. Keselowski is 27 points out of the lead, while Kenseth trails his teammate by 36 markers.
Sunday's 500-mile race at Texas is scheduled to start just after 3:00 p.m. (et).