Georgia native Kuchar lacked the sharpness off the tee he had so impressively delivered in the previous round and his challenge for a maiden major victory ended as he carded a two-over-par 74 to tie for fifth place.
Fowler, also hunting his first grand slam crown, finished level with Kuchar at two under after hitting only four of 14 fairways on the way to a closing 73.
"The driver was not near as sharp today," Kuchar told reporters, having briefly moved into a tie for the lead with birdies at the second and third before his challenge unraveled.
"I hit what I thought were a couple of decent drives. At nine, I thought it was a decent drive, caught some trees. On 18, the same thing. On 11, I missed the fairway.
"It seemed to miss the fairway just by little bits here and there. My driving was not nearly as sharp as it was yesterday and hard to play really good golf out here if you're not playing from the fairway."
Kuchar, who won two big events on the PGA Tour last year, including his first World Golf Championship (WGC) crown, never got back into contention after four-putting to double-bogey the par-three fourth.
"It was a setback, but it wasn't too much to overcome. It put me back to even par after three or four holes. It's not the worst thing to be even par through four.
"I knew in golf you have ups and downs," the 35-year-old said after a round that included three birdies, three bogeys and the double. Those things happen.
"I can't recall the last time I four-putted. But if there was ever a place to do it, it was there."
Asked what he would take away took from Sunday's final round, Kuchar replied: "It's an exciting place to be, but it's a tough one. I don't know how many opportunities you get at winning the Masters tournament.
"And I've had two this far, and I don't know how many more I'll get. It's one of those things you get in the situation and you hope to take advantage but it's a lot better in this position than playing early on Sunday, that's for sure."
Fowler surprised himself that he was able to sign for a 73 after struggling so badly off the tee.
"It was a rough driving day for me," said the 25-year-old whose only PGA Tour victory came at Quail Hollow in 2012. "But I definitely got a lot out of the round with how poorly I got it off the tee.
"I got off to a nice start and had a good look (for birdie) on two, and had a tough break with a lip-out. Actually two good putts, and I walked away with a bogey. Kind of a tough way to start.
"Yeah, just drove it poorly today, so that kind of kept me from being able to attack the golf course."
While Fowler had to settle for a share of fifth place in the season's opening major, he was delighted that his good friend, Bubba Watson emerged triumphant at Augusta National for a second time in three years.
"This place suits him perfectly," said Fowler. "He's able to hit golf shots around here that some guys can't, so this place fits him perfectly. It's fitting for him to win here."