Newman posted a lap at 122.811 mph around the half-mile, high-banked Bristol track for his second pole of the season and the 48th of his Sprint Cup Series career. He started on the pole and won last month at New Hampshire Motor Speedway.
"It was a good lap, but it didn't feel that fast," Newman said. "We're in a good position right now, but we just need to make the best of it. We got a lot of things going our way. This is a track position race. We're starting up front and have a good pit selection. We just need to keep our nose clean tomorrow night."
Newman began his week at Bristol by winning Wednesday's NASCAR Whelen Modified Tour race.
Edwards' qualifying lap was 0.02 of a second slower than Newman's.
"It was a fun lap, but I can't believe Ryan got me," Edwards said. "He did a really good job. My guys did a good job. It's a good starting spot, but we wanted that pole bad."
While Newman claimed his third Sprint Cup pole at Bristol, his Stewart-Haas Racing teammate, Tony Stewart, finished last in the 46-car field for qualifying. Stewart will start 42nd based on owner points. He is currently 10th in points and has yet to win a race this season. Just three races remain before the championship Chase begins.
Kyle Busch, the current points leader and winner of last Sunday's race at Michigan, will start 23rd. Busch has won four of the last five races at Bristol, including the previous two.
T.J. Bell, J.J. Yeley and Jeff Green failed to qualify.
Saturday's 500-lap race at Bristol is scheduled to start just after 7:30 p.m. (et).