The Cardinals capitalized on three walks from Minnesota relievers to score four runs in the top of the seventh inning, but Clemens responded with a game-tying blast in the bottom half.
After St. Louis reclaimed a one-run lead in the top of the eighth, Royce Lewis tied the game again with a mammoth home run into the second deck of the left-field stands.
According to FanGraphs data published before the game, the Cardinals hold an over 50% chance of making the postseason while maintaining a 2.5-game lead in the first National League Wild Card spot.
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Minnesota will start Connor Prielipp against St. Louis pitcher Matthew Liberatore in the second game of the series on Saturday.