Scott, who had a four-round total of 14-under 270, will now try to win the so-called Australian Triple Crown with a victory at the Australian Open at Royal Sydney in two weeks. Before that, he will partner Jason Day for Australia at the World Cup next week, again at Royal Melbourne.
Kuchar took the lead when Scott made a double bogey on the 14th as he dealt with a plugged lie in a bunker, while Kuchar in the preceding group made a birdie at the 15th.
The situation was reversed a whole later when Scott also birdied the 15th and the American bogeyed the 16th.
Scott had led by four strokes at the start of the round and by five shots late on the front nine.
His faltering on the back nine revived memories of the 2012 British Open when he bogeyed the final four holes to lose by a shot, but this time he came out on top.
"I usually like looking at the leaderboard, but it wasn't enjoyable today," Scott said of the numerous lead changes. "I made a lot of errors, but I managed to hang on despite being a little shaky out there."
His day got off to an ominous start. His birdie putt from three feet lipped out while Singh had a tap-in birdie to reduce the lead to three, but a Singh bogey on the second restored the four-shot gap.
While Scott and Singh dueled in the final group, Kuchar, who will team with Kevin Streelman for the United States at the World Cup, moved up the leaderboard.
The American bogeyed the first hole, but birdies on five of the next eight holes left him as Scott's closest pursuer. He birdied the 11th and then the 15th to take the lead for the first time in the tournament before his late collapse.
"It's never fun, the 72nd hole, but it can happen any time," Kuchar said. "I tried on the last hole to stay aggressive and hit a good quality shot and I thought I had.
"The thing about Royal Melbourne is you can really pay the price for just being off if you play aggressively. It's certainly a rough way to end it but that's kind of the nature of the game."
Jarrod Lyle, playing in his first tournament in 20 months since his recovery from his second bout of leukemia, finished with an 8-over 79, including bogeys on his final three holes. He didn't expect to make the cut.
At the 18th, the large gallery applauded, even playing partner Michael Long, as Lyle walked gingerly around the green.
"I played five days in a row, including the pro-am, and the last nine holes I started to feel it," Lyle said. "I got around, and it's not the end I wanted. But it's better than I thought it would be: three good rounds and one shocker, that's golf."
- AP
