La Russa noted that Bradley had "centered" the ball in his previous two at-bats in lining out to right and to left. On this occasion, Bradley lined to right to end the game.
Wainwright (4-2) said he had wanted to stay in the game "more than you know. I didn't want to give him that ball. But he's been managing for a long time."
In his last two outings, Wainwright has changed his release point and has given up only two runs in 16 2/3 innings.
"The ball is coming out of my hand with a whole lot more life than before," Wainwright said.
Franklin's 11th save wrapped up a series in which the Cardinals outscored the Cubs 8-2.
One of the offensive stars Thursday was third baseman Brian Barden, who had been 6-for-32 at Busch Stadium before homering off Cubs lefty Sean Marshall in the fourth inning. Another was first baseman Albert Pujols, who knocked out the lights in the "I" in the "Big Mac Land" sign in left-center field with a 418-foot laser beam homer in the first.
"I hope they don't repair that," La Russa said. "It's such a signature thing.
"That was a line drive. That wasn't a home run. It proves how far you can hit a line drive."
CARDINALS 3, CUBS 1: 1B Albert Pujols homered for the 14th time this season and sixth time in his first at-bat of a game. RHP Adam Wainwright wrapped up a brilliant stretch of starting pitching in which Cardinals starters allowed the Cubs only one run in 22 2/3 innings, and St. Louis completed its first three-game sweep of Chicago at home since Aug. 25-27, 2006.