Wainwright (15-8) came into the game with the most wins in the National League, but he retired only six batters while giving up nine runs on eight hits.
Cincinnati sent 10 men to the plate in the first while scoring six runs, the first two coming in on a single by Bruce. Ryan Ludwick, Todd Frazier and starting pitcher Homer Bailey all drove in a run in the opening inning and the Reds came up with another score on a wild pitch.
The result tightened the National League Central race with the St. Louis lead over Pittsburgh being reduced to a half game. Cincinnati is 3 1/2 games behind the Cardinals.
Bailey (9-10) gave up five hits and struck out seven over 7 1/3 innings to get the win. The shutout was completed by J.J. Hoover and Sam LeCure.
Kim Kardashian, Kanye West reportedly set wedding date
NBC reportedly holds celebs hostage to Jimmy Fallon's show