Martin, at age 53, won the 53rd pole of his career. He turned in a lap of 128.327 mph while making the final qualifying attempt among the 45 drivers entered.
He became the second two-time pole winner on the circuit this year, joining Kasey Kahne. Martin also won the pole in Phoenix last month.
Edwards will start on the outside of the first row in Saturday's race, followed by Kevin Harvick, A.J. Allmendinger and Kyle Busch. The rest of the Top 10 was made up of Jeff Gordon, Denny Hamlin, Martin Truex, Jr., Kahne and Dale Earnhardt Jr.
Current points leader Greg Biffle qualified 28th.
Megyn Kelly: Santa Claus and Jesus are both white men
Video of Victoria’s Secret models trying to 'twerk' hits Instagram