Matt Holiday led off the frame with a hit off Rafael Dolis (2-3) and one out later advanced to second on a David Freese groundout.
That set up Molina, who sliced a three-hopper past diving Cubs second baseman Darwin Barney, sending Holliday (3-for-4, home run) home with the game-winner as St. Louis a split in its two-game set at Busch Stadium.
Matt Carpenter cracked a solo homer in the eighth that briefly handed the Cards a 6-5 lead, but Chicago's Alfonso Soriano responded with a bases-empty blast in the next half-inning off Jason Motte (2-1), again knotting the contest.
Allen Craig went 3-for-4 with two RBI in the victory.
Bryan LaHair hit is 10th homer of the year for the Cubs.