The 48-year-old carded eight-under-par to finish 10-under for the tournament and speaking after his round Mickelson admitted he hopes he's done enough to gain a spot on USA's Ryder Cup team.
"Not that it was an easy decision", Furyk said with a smile.
Bryson DeChambeau's unorthodox approach to golf has prompted a lot of second guessing over the years.
DeChambeau, 24, had virtually guaranteed himself one of the captain's picks after storming to victory in the opening two legs of the PGA Tour's FedEx Cup playoff series, winning the Northern Trust and Dell Technologies Championship.
The win guaranteed that DeChambeau will be the top player in the playoff standings when the season concludes at the Tour Championship in three weeks in Atlanta, regardless of how he finishes next week at the BMW Championship in suburban Philadelphia.
Perhaps of more importance, DeChambeau's victory looks to have cemented his place in the United States Ryder Cup team as one of four wildcard picks. He was one shot out of the lead on the front nine until a bogey on the par-5 seventh hole, and three more bogeys in five holes to start the back nine.
"I've had quite a bit of resistance", DeChambeau said.
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During the FedEx Cup playoffs, he was runner-up at one event and tied for fourth at the other.
You can see who Thomas Bjorn selects with his four captain's picks on Wednesday at 2pm (BST) - we'll be covering the announcement live on The Sportsman. Still to be determined was whether former Masters champion Sergio Garcia, who failed to qualify for the FedEx Cup playoffs, gets a nod.
Ton Finau, Xander Schauffele and Kevin Kisner are all in contention to join the aforementioned trio and automatic qualifiers Brooks Koepka, Patrick Reed, Rickie Fowler, world no 1 Dustin Johnson, Jordan Spieth, Webb Simpson, Justin Thomas and Bubba Watson. Throw in Woods and Mickelson, and that gives the USA team a lineup that has combined for 31 majors.
"We're heading over into foreign soil", Furyk said.
"That's something I've been working on doing for a long time and hopefully I can get closer to that number one spot".
"It's going to be a great challenge because we know how strong the European side is and how well they play at home. And naming these three players, that's what we've done".