THOUSAND OAKS, Calif. — Graeme McDowell kept trying to convince himself and everyone else that his game was improving, even though he had gone two years without a trophy to prove it.

That’s what made Sunday at Sherwood so sweet.

With a pair of superb short-game shots on the back nine, McDowell closed with a 4-under 68 to win the World Challenge by three shots over Keegan Bradley, allowing him to head home for a 10-week break with a shot of confidence.

“It’s been too long. It’s been a hell of a two years since I sat here as a winner,” McDowell said. “We all put winning up on a pedestal as the ultimate goal. We like to say that it’s all about the process and going through the motions and trying to get better. But let’s be honest. We all measure ourselves by the win. I can say that now.”

The three-shot margin made it look easier than it was.

Sherwood was playing longer than ever in a light rain, giving an advantage to a big hitter like Bradley, not to mention tournament host Tiger Woods. Even when McDowell built a four-shot lead through 11 holes, a careless three-putt bogey on the 13th brought Bradley within two shots with five holes to play.

McDowell responded with a 75-foot putt that he lagged to tap-in range, a key moment for someone coming off a three-putt bogey. From a precarious spot behind the 17th green, he had to land his chip in the rough and hope it would hop onto the fringe and not run to far by the hole. He pulled it off perfectly.

“It was an inch away from sticking in the fringe, and about 1-16th of an inch away from going in the hole,” he said.

He made one last birdie he didn’t need, extending his dominance at Sherwood. It was the 10th time in 12 rounds at Sherwood that McDowell has shot in the 60s, and he now has two wins and a runner-up finish in his three trips to the World Challenge.

“This really caps off my season,” McDowell said. “We try not to put winning on a pedestal, but this one feels very sweet because it’s been a grind all year.”

McDowell won for the first time since he beat Woods in a playoff at Sherwood to close out a dream season in 2010 that included his first major at the U.S. Open and the winning point for Europe at the Ryder Cup.

This win followed a year of frustration. He played in the final group of the U.S. Open and British Open but came up short, and he lost some enthusiasm going into tournaments late in the year. He talked all week about a 10-week break, some of it in Northern Ireland and the rest in Orlando, Fla., where he just built a new house and he’s opening a tavern outside the gates of Lake Nona. Bradley, who was within one shot after a birdie on the fifth hole, closed with a 69. Bo Van Pelt had a 70 to finish third.

Also on Sunday:

Kaymer wins by two strokes at Nedbank Challenge

SUN CITY, South Africa — Martin Kaymer of Germany shot a 3-under 69 to earn his first title of 2012, holding on for a two-shot victory in rainy conditions at the Nedbank Golf Challenge. Kaymer finished at 8-under 280, two ahead of Charl Schwartzel (69) of South Africa. Bill Haas of the United States was third after a 71.

Australian up one at PGA Tour qualifying tourney

LA QUINTA, Calif. — Australia’s Steven Bowditch shot an 8-under 64 on PGA West’s Jack Nicklaus Tournament Course to take a one-stroke lead after the fifth round of the PGA Tour qualifying tournament. Bowditch had a 23-under 337 total in the six-round event. The final top 25 and ties will receive 2013 PGA Tour cards.

Two top LPGA Tour qualifying event

DAYTONA BEACH, Fla. — Canada’s Rebecca Lee-Bentham shot a 5-under 67 to tie Thailand’s Moriya Jutanugarn for the top spot in the LPGA Tour qualifying tournament, leading the 20 players who earned full status. Lee-Bentham and Jutanugarn finished the five-round event at 13-under 347 at LPGA International. Jutanugarn shot a 74 after taking a six-stroke lead into the day.