Cole (6-6) extended his winning streak to three games, allowing five hits and one run with five strikeouts and two walks.
In Cole's four losing starts from May 22 through June 8, he surrendered 23 runs in 19 1/3 innings. Since then, he has reeled off three solid starts. Before Saturday, he allowed just three hits and one run in seven innings in each of his previous two starts.
Pittsburgh has won four of its last six games.
Slumping St. Louis has dropped eight of its last 11. The 33-40 start for the Cardinals is their worst since 2007.
