To the delight of his watching family, Kuchar shot a final round two-under 70 to finish 13-under for the tournament, two clear of Briton Martin Laird (67) and Americans Zach Johnson (68), Rickie Fowler (70) and Ben Curtis (68).
Overnight leader Kevin Na had a disappointing finish, making six bogeys in a 76 that saw him slip back into a tie for seventh, a day after being heckled by spectators for his slow play and constant practice shots.
Tiger Woods ended well down the field at joint 40th after shooting a 73 to finish one-under.
England's Luke Donald finished strongly with a 66 that elevated him to sixth, four strokes behind Kuchar, but not enough for him to regain top place in the world rankings from Northern Irishman Rory McIlroy, who missed the cut.
Kuchar, who tied for third at the Masters, consistently avoided trouble on the final day on a course that severely punishes inaccuracy.
While his challengers stumbled at various hurdles, the American kept out of water and greenside sand throughout a confident 18 holes.
"You think of this as one of the strongest fields in golf and to come out as champion is an amazing feeling," the 33-year-old told reporters.
Kuchar, who found 10 of 14 fairways and struck 15 greens in regulation, wrapped up the tournament when he coolly sunk a 15-foot birdie putt on the 16th to surge three strokes clear.
Although bogeying the 'island green' 17th, the fixed grin never left his face as he went to the final tee with a two-shot cushion.
Fowler's second place finish was the fifth of his career and followed his maiden US PGA Tour win at Quail Hollow last week.
The 23-year-old made a late charge with birdies on the 16th and 17th holes but missed a nine-foot birdie putt on the 18th that would have put more pressure on Kuchar.
Kuchar safely parred the last to claim his first US title win since the 2010 Barclays at the Ridgewood Country Club in New Jersey.
"I saw Rickie's putt on 17 and I knew it got him to within two shots and he could birdie 18 to reduce it to one. That could have changed the whole scenario of how I would play the last hole," he said.
"So I was really excited to drop that birdie on 16. That was big," he added.
For Fowler, despite falling short, it was another reminder of his emergence in the game.
"It was a lot of fun to be in contention and I tried to give it a run at the end. Kuch played very well, very solid and I just fell a couple of shots short," he said.
"I've had a lot of confidence in my game which has given me the calm you need coming down the stretch when the nerves are supposed to be on."
Scotsman Laird, who started the day six back, made an early challenge with six birdies through 13 holes, including a trio on 11, 12 and 13, but his push faded with bogeys at 14 and 18.
"I found my confidence this week for some reason. This is my best finish in a big, big marquee event," said the United States-based Glaswegian.
For the third tournament in a row, Woods failed to mount a challenge. He also finished tied for 40th at the Masters before missing the cut at Quail Hollow.
"I've just got to keep working, keep working. I felt that I did it well in spurts again," Woods said. "I just need to be a little bit more consistent."