Rookie right fielder Steve Selsky led the assault, going 5-for-5 with two runs and four RBIs. Left fielder Adam Duvall went 4-for-6 with four runs and five RBIs, giving him 100 RBIs for the year, and second baseman Brandon Phillips went 4-for-5, the 14th four-hit game of his career.
Not to be outdone, rookie pitcher Tim Adleman (3-4) went seven strong innings, allowing four hits and two runs with no walks and four strikeouts.
Jaime Garcia (10-13) lasted just one inning in his first start since Sept. 13, yielding four hits and two runs as he dropped his fifth straight decision.
Cincinnati improved to 66-90 and St. Louis (81-75) dropped a game behind idle San Francisco with six games left. It remained 1 1/2 games behind the New York Mets, which lost 7-3 in Miami, for the first wild card.
Cincinnati started the onslaught with two-out solo homers in the first by Joey Votto and Duvall, then made it 3-0 in the second when Selsky cracked a leadoff homer into the seats in right center.
The Reds turned it into a laugher with seven runs in the fourth, six with two outs. Jose Peraza lofted a sacrifice fly, Eugenio Suarez followed with an RBI single and Duvall poked a run-scoring single two batters later.
Phillips tacked on a two-run single. Selsky produced an RBI single and Tucker Barnhart capped the eight-hit outburst with a run-producing single.
St. Louis managed to get on the board in its half of the fourth on a sacrifice fly by Yadier Molina, but Cincinnati plated four more in the fifth. Duvall walloped a three-run homer, giving him his third two-homer game of the year, and Selsky rapped his fourth hit, an RBI single.
Jedd Gyorko scored Jhonny Peralta in the Cardinals' half of the fifth with a single to center.
NOTES: St. Louis SS Aledmys Diaz traveled to Miami on Monday to grieve with the family of Jose Fernandez, the Marlins' All-Star RHP who died in a boating accident early Sunday morning. Diaz flew back to St. Louis late Monday afternoon to be available for the game. ... Cincinnati placed SS Zack Cozart (knee) on the 15-day disabled list, retroactive to Sept. 16. Cozart batted .252 with 16 homers and 50 RBIs this year. ... Cardinals INF Matt Carpenter, mired in a 1-for-16 slump, did not start Monday night. Greg Garcia got the call at 2B.