He was briefly tied for the lead after carding a bogey-free eight-under-par 62 at Sedgefield, but eventually had to settle for a share of third place, two strokes behind winner Arjun Atwal.
"That's the best back-to-back ball-striking rounds I've had in a while," said Sim, who started the final round seven strokes from the lead.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"I've been struggling with my ball-striking all year and it really came around this week. My putting's been fantastic and that continued."
Atwal, 37, made history, becoming the first player from India to win on the US PGA Tour.
He started the final round with a three-stroke lead, but had to work hard to fend off the charging pack in ideal scoring conditions.
Atwal, who is coached by Australian Dale Lynch, came to the last knowing he needed a par to win. He fired his second shot over the back of the green and then chipped his next to two metres, from where he sank the pressure-packed par putt.
He carded 67 to finish at 20-under 260, one stroke ahead of fast-finishing American David Toms (64), who birdied three of the final four holes.
Atwal, who did not have exempt status on tour, only got into the tournament by winning one of four spots up for grabs at a qualifier last Monday.
He is the first Monday qualifier to win on tour since 1986.
His victory, worth $US918,000 ($A1.03 million), earns him a two-year exemption and a spot in next year's Masters. He is also likely to get a congratulatory text message from his good friend Tiger Woods.
Marc Leishman (64) and Aron Price (65) were best of the other Australians, equal 18th on 14-under 266.
"I went at every pin and was aggressive with all the putts," Leishman said.
