The Spanish golfer won his first US PGA Tour title in four years to guarantee himself a place in Jose Maria Olazabal's team.
Sergio Garcia books Ryder Cup place with victory in Wyndham Chmpionship
Garcia, one of 38 players returning to the course to complete a final round halted by rain, carded a 66 for an 18-under par total of 262.
It was Garcia's first US title since he won the 2008 Players Championship, and his first title worldwide since his back-to-back victories on the European Tour last October.
"Obviously I won a couple of times last year in Europe, but it's been a while here (in the United States) and it feels great," he said.
Garcia started the week at 11th on the world points list, and his win took him to sixth on that list and eighth in the overall European Ryder Cup selection standings.
With just one more eligible event remaining at Gleneagles he can't be pushed out of the top 10 automatic qualifying spots.
European captain Jose Maria Olazabal will also make two captain's picks for the team for the biennial match-play showdown.
Garcia led after the third round and was atop the leader board when fourth-round play was suspended Sunday because of heavy rain.
After a bogey dropped him into a tie for the lead the Spaniard birdied four holes in a five-hole stretch to regain the advantage.
Garcia began his march to the title with a birdie at 13, where he chipped to about a foot and made the putt for birdie.
He birdied 15 from a bunker, sinking a five-foot putt, and birdied the par-three 16th after his tee shot landed two feet from the pin.
His birdie at 17 moved him to 19-under, making a bogey at the last meaningless.
"I am proud of the way I played coming in," Garcia said.
The victory helped erase the memories of his last appearance at Greensboro, when he held a share of the third round lead in 2009 but eventually finished fourth.
"That year, I was pretty much in control and I lost it myself," Garcia said, adding he didn't think the Sedgefield course owed him something. "The course didn't do anything wrong to me."
Clark, a local favourite after attending North Carolina State University, moved into a tie with Garcia with a birdie at the eighth — his third hole of the day.
Garcia edged ahead again with a birdie at the 11th, but after a bogey at 12 he was again tied for the lead.
American Chad Campbell briefly joined them atop the leader board with a third straight birdie at 17, but Garcia then launched his big run.
American Bud Cauley finished third with a 68 for 265. Campbell's 66 gave him a share of fourth place on 266 alongside Jimmy Walker (67) and Sweden's Carl Pettersen (68).
"It was going to be tough to catch (Garcia), the way he finished," Clark said.
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