The 34-year-old seized an early advantage at the fourth hole with a calm birdie to put Mahan behind for the first time in the tournament.
Mahan slipped away and was four down after nine holes but battled back to within a single shot in the closing stages.
Kuchar maintained his composed approach to hit a superb bunker shot at the 18th before sinking a six-foot putt to claim the title.
Mahan narrowly missed out 2&1 in the first all-American final in the competition for nine years as Kuchar added the matchplay crown to his Player's Championship from last season.
Englishman Ian Poulter rounded off a disappointing day by losing the third-place playoff to Day by one shot.