Overnight leader Rickie Fowler missed out on an automatic Ryder Cup place after carding a three-over round of 74 on Sunday to finish joint seventh.
Fowler needed to finish third and will now hope to be a wildcard pick on Davis Love's team.
Reed, on the losing team at Gleneagles in 2014, said: "I want sweet revenge, just like our whole team does."
Europe have won the competition three times in a row, and eight times in the last 10.
Reed, 26, beat fellow American Sean O'Hair and Argentina's Emiliano Grillo by a shot in New York to go top of the PGA points standings.
Scotland's Martin Laird ended two under par, while England's Olympic champion Justin Rose and Northern Ireland's Rory McIlroy finished on level par.
Reed, who represented the USA at the Presidents Cup in South Korea and at the Olympic Games in Brazil, added: "I finally get to play for the United States in the United States and I cannot wait to see how the fans are, and just have the whole crowd on our side this time."
Fowler's late slip-up saw 2015 Open champion Zach Johnson claim the final automatic spot.
1. Dustin Johnson
2. Jordan Spieth
3. Phil Mickelson
4. Patrick Reed
5. Jimmy Walker
6. Brooks Koepka
7. Brandt Snedeker
8. Zach Johnson
Captain Davis Love has four wildcard picks and will choose three after the BMW Championship on 11 September.
Love will make his final selection two weeks later after the Tour Championship, only five days before the Ryder Cup starts on 30 September.
Among those in contention for a spot, along with Fowler, are Bubba Watson, who finished ninth in the standings, and JB Holmes.
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Patrick Reed won his first tournament of the season at The Barclays to seal his spot on the USA Ryder Cup team.