David Goldman / AP Photo

Adam Scott finished the job this time, and put an end to more than a half-century of Australian misery at the Masters.

With the two biggest putts of his career, the former UNLV golfer holed a 20-footer for birdie on the 18th hole of regulation that put him into a playoff with Angel Cabrera, and then won his first major championship Sunday with a 12-footer for birdie on the second extra hole.

“We like to think we’re the best at everything. Golf is a big sport at home, and this is the one thing in golf we hadn’t been able to achieve,” said Scott, who golfed one season at UNLV in the late 1990s. “It’s amazing that it’s my destiny to be the first Australian to win. It’s incredible.”

Scott leaned back and thrust his arms in the air after the putt dropped on the 10th hole, a celebration for all of Australia and personal redemption for himself. Also, he became the first UNLV golfer to win a major tournament championship.

It was only last summer when Scott threw away the Open Championship by making bogey on his last four holes to lose by one shot to Ernie Els. The 32-year-old handled that crushing defeat with dignity and pledged to finish stronger given another chance. “Next time — I’m sure there will be a next time — I can do a better job of it,” he said that day.

Scott was close to perfect, and he had to be with Cabrera delivering some brilliance of his own.

Moments after Scott made his 20-foot birdie putt on the 18th hole for a 3-under 69 to take a one-shot lead — “C’mon, Aussie!” he screamed — Cabrera answered with an approach that plopped down 3 feet from the cup, one of the greatest shots under the circumstances. That gave him an easy birdie and a 2-under 70. They finished at 9-under 279.

They both chipped close for par on the 18th in the first playoff hole, and Cabrera’s 15-foot birdie putt on the 10th grazed the right side of the cup.

With his long putter anchored against his chest, Scott’s putt was true all the way. The Masters had been the only major that never had a champion use a long putter. Scott’s win means four of the last six major champions used a putter pressed against their belly or chest, a stroke that might be banned in 2016.

What mattered more to Scott was that the Masters had been the only major an Australian had never won. He was among dozens of golfers who routinely rose in the early hours of Monday morning for the telecast, only to watch a horror show. The leading character was Greg Norman, who had four good chances to win, none better than when he blew a six-shot lead on the last day to Nick Faldo in 1996.

There was Jim Ferrier in 1952 and Bruce Crampton 20 years later. Scott and Jason Day tied for second just two years ago. Norman, though, was the face of Aussie failures at the Masters, and Scott paid him tribute in Butler Cabin before he slipped on that beautiful green jacket.

“Australian is a proud sporting nation, and this is one notch in the belt we never got,” Scott said. “It’s amazing that it came down to me today. But there’s one guy who inspired a nation of golfers, and that’s Greg Norman. He’s been incredible to me and all the great golfers. Part of this belongs to him.”

Scott was just as gracious in victory as he was last summer at Royal Lytham & St. Annes. He and Cabrera flashed a thumbs-up to each other after their shots into the 10th hole in the playoff, and they walked off the 10th green with their arms around each other when it was over.

“Such is golf,” Cabrera said. “Adam is a good winner.”

It was a riveting conclusion to a week filled with some awkward moments. There was the one-shot penalty called against 14-year-old Tianlang Guan that nearly kept the Chinese teen from becoming the youngest player to make the cut. There was the illegal drop by Tiger Woods, who was given a two-shot penalty over questions and confusion about why he was not disqualified for signing an incorrect card.

And at the end, there was shot-making at its finest.

Scott didn’t make a bogey after the first hole, and he really didn’t miss a shot the rest of the day on a rainy Sunday at Augusta. He just couldn’t get a putt to fall until it really mattered. Then, he made two of them.

Day closed with a 70, his second close call at the Masters in three years. This one hurt far more because he had a two-shot lead when he stepped to the 16th tee.

He ran off three bold birdies down the stretch — getting up-and-down from the back bunker on the 13th, a 10-foot putt on the 14th, and capitalizing on a break at No. 15 when his drive ricocheted out of the trees into the fairways, allowing him to reach the green in two.

His lead vanished just as quickly, however. Day chose to hit putter from behind the 16th green, came up 5 feet short and missed the par putt. He hit into a bunker on the 17th for another bogey.

“I think the pressure got to me a little bit,” Day said.

The tournament unfolded behind him, and it turned out to be quite a show.

Scott hit the ball beautifully the entire day and watched one putt after another turn away from the hole. But he also received perhaps the biggest break of the tournament when his shot into the par-5 13th spun back off the green and was headed down the slope into the tributary of Rae’s Creek when it suddenly stopped, a blessing from a day spent in the rain. He got up-and-down for birdie, and he two-putted for birdie on the 15th.

Cabrera wasn’t so fortunate. Playing in the group behind, his approach hit the bank and tumbled down into the water, leading to a bogey that cost him the lead. Cabrera answered with a 15-foot birdie putt on the 16th, however, that gave him a share of the lead.

And then came a one-two punch of birdies. For the fans who endured a soggy final round, this made up for it.

Two players. Two clutch birdies. Two different celebrations.

Scott screamed at the top of his lungs, “C’mon, Aussie!” and clapped hands forcefully with caddie Steve Williams when his 20-foot birdie putt curled around the left side of the cup -- just like Phil Mickelson’s winning putt in 2004 -- and dropped in the back.

Scott was in the scoring room when he looked up and saw Cabrera chase after his approach, pumping his fist when his 7-iron plopped down 3 feet from the cup for a birdie. Cabrera affectionately hugged his son and caddie, Angel Jr., as they walked off the green toward the scoring room.

“It was a split second I thought I’d won,” Scott said. “That was the putt we’ve seen so many guys make to win, and what I thought is it’s time for me to step up and see how much I want this. To make a couple putts to win the Masters is just an amazing feeling.”

Brandt Snedeker, tied with Cabrera for the lead going into the final round, closed with a 75 and finished five shots behind.