The Reds came out swinging a few hours after Brandon Phillips' expletive-filled tirade at a Cincinnati Enquirer reporter sparked by scrutiny of his .310 on-base percentage, and after manager Dusty Baker criticized his team for falling short while dropping four of five.
The Cardinals lead the NL Central by a half-game over Pittsburgh after losing for the third time in 12 games, and the Reds are 3 1/2 games back.
Bailey (9-10) capped a six-run first against Adam Wainwright (15-8) with the Reds' sixth hit and his first RBI of the season. He allowed five hits in 7 1-3 innings with seven strikeouts and is 4-0 in his past six starts.
The poor start was unusual for Wainwright, who matched his career worst with nine runs allowed and lasted two innings for his shortest outing of the year.
He had worked at least seven innings his previous eight starts and was coming off a complete game against the Braves.
Phillips singled his first two at-bats and struck out his next two trips while going 2 for 5.
The Reds also got RBIs from Ryan Ludwick and Todd Frazier in the first with another run scoring on a wild pitch. Zack Cozart got the first of his three hits when Wainwright failed to cover first.
Phillips singled and Joey Votto walked again to open the second, setting the table for Bruce's 26th homer on a 1-2 pitch. It's his third five-RBI game, one of them against the Cardinals in 2009.
Rookie Michael Wacha was a bright spot for St. Louis, following Wainwright with four scoreless innings and seven strikeouts.
Shortstop Pete Kozma was among four substitutes in the sixth with the Reds still up 9-0, going to left field in his first appearance as an outfielder since July 28, 2007, when he played right field for Class A Gulf Coast.
Chris Heisey put the Reds in double figures with his 10th homer off Fernando Salas in the ninth.
Notes: Votto entered just 3 for 23 with one RBI and one walk against Wainwright. ...The Reds have won three of the past 11 in the series. ... Cardinals pitcher Chris Carpenter, out all season with a nerve ailment, accompanied the team on its last trip to serve as a mentor after manager Mike Matheny said he "realized he could bring value." Matheny was hopeful the pitcher would make the next trip, too.