The Cardinals scored nine times during the first two innings to move closer to a wild card playoff spot.
St. Louis began the night with a three-game lead over the Los Angeles Dodgers in the battle for the second wild card position in the National League.
Washington starter Edwin Jackson (9-11) was hammered for eight earned runs while retiring only four batters. Jackson issued a bases-loaded walk to Carlos Beltran in the first inning, which also included run-scoring singles from Allen Craig and Pete Kozma.
Craig also had an RBI base hit during St. Louis' four-run second.
Despite the loss Washington stayed four games in front of Atlanta in the National League East with five to play. A win by the Nationals and a loss by the Braves on Saturday will give Washington the division crown.
Adam Wainwright (14-13) picked up the victory, surrendering one run on five hits in six innings.