By making the final, Harman and Cox qualify for the U.S. Amateur that begins Aug. 18 at Oakmont.
Cox, 15, was trying to overtake Tiger Woods as the youngest champion in the event's history.
Harman applied early pressure, making a 25-foot birdie putt at the 357-yard, par-4 third hole. That birdie began a stretch in which Harman won six of the next eight holes to lead 5-up after 10. His clinching par on the 14th came on a 2-foot putt.
'I'm such a streaky player that if I get up one or two, I'm gone,' said Harman, who was taken to 20 holes in his first-round match. 'It's kind of mean, but you've got to do it. You can't have a heart out there, especially if you're trying to win a championship. You just play you're heart out and try to beat him into the ground if you can.'
Just 1-down after sinking a 30-foot eagle putt at the previous hole, Cox was in the center of the fairway at the sixth with Harman off to the left, blocked by trees. Both players missed the green, but Cox was left with the better lie. Harman got the ball within 12 feet of the hole and Cox misplayed a chip, allowing the hole to be halved with bogey-5s.
'It was partly my mistake from the fairway, but I didn't think the chip was going to be that fast,' Cox said. 'I was a little disappointed, but you win a hole, you lose a hole. That's just the way it is in match play.'
Harman won the next four holes, and Cox captured just one more hole the rest of the way.
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