Edwards, who won last week at Memphis to move within 116 points of Bowyer with three races left, earned his fourth pole of the season Friday night at the 1 1/2-mile high-banked Texas track with a lap of 188.101 mph in his Ford.
Bowyer, who finished third in the April race at Texas, was nearly 5 mph slower in his Chevrolet and qualified 21st for Saturday's O'Reilly Challenge.
Kevin Harvick qualified second with a lap of 186.587 mph, ahead of Bobby Hamilton Jr. and Kyle Busch, who won the Nationwide race at Texas in April.