MINNEAPOLIS — Aaron Hicks made the biggest catch of the Yankees’ season — a full-extension diving grab at the warning track with the tying and winning runs on base Tuesday night — in one of baseball’s most exhilarating games of the season.

Hicks’s jaw-dropping play ended a heavyweight battle between the Yankees and the Minnesota Twins, two of the best teams in the major leagues. Two high-powered offenses landed blow after blow against the opposing pitching staffs, and then kept punching.

Every out felt like an enormous task. Every base runner added more chaos. There were five lead changes, 26 runs and four blown saves.

Then, with the bases loaded in the bottom of the 10th inning, the Twins’ power-hitting center fielder, Max Kepler, laced a 97-mile-an-hour fastball from Chad Green deep into the left-center-field gap.