Yadier Molina made his third Grapefruit League start, but he once again didn't swing the bat in his only at-bat. Molina, who is recovering from two offseason thumb surgeries, left the game for a pinch-hitter in the fifth.
Max Kepler's two-out single to center in the top of the seventh drove home Darin Mastroianni, breaking a 2-2 tie.
The Twins touched up Leake's replacement, Seth Maness, for two runs in the fifth, the second run scoring when Jorge Polanco's hot shot to first took a bad hop, forcing first baseman Matt Holliday to defensively knock the ball down.