Right when it looked as though Zach Johnson had played his way off the US team, Fowler squandered a chance to earn the eighth and final automatic spot when he shot 39 on the back nine at The Barclays, capped off by two bogeys and a double bogey over his last four holes.
"I don't think there was a tee shot that I felt comfortable over to be honest", Day said.
Through 14 holes playing alongside Reed on Sunday, Fowler looked like he wasn't going to win the golf tournament, but he would at least find a way on the Ryder Cup team again.
He will then make his fourth and final pick at the end of the Tour Championship.
Rickie Fowler had been one shot ahead of the final round, but couldn't maintain his lead, finishing equal seventh.
"I didn't drive the ball the way I needed to", Fowler said.
"This is about as tough a test as you get and I did great the first 10 holes", said Fowler, who also took bogey at the 18th.
Reed later said that short stretches of poor play had cost him several chances to win in recent times, but the difference on Sunday was that he had a cushion coming down the stretch. Bernhard Langer made a 3-foot birdie putt on the first hole of a playoff with Woody Austin and Kevin Sutherland to win the PGA Tour Champions' Boeing Classic in Snoqualmie, Washington, for the second time.
Joint runner-up Grillo, who finished tied for 13th at the PGA Championship at Baltusrol last month, had thought pre-tournament that seven-under would have a chance of winning on a public course that bears a warning sign that it is "only for highly skilled players". While a birdie at 17 revived his faint Ryder Cup hopes, he bogeyed the last to card a 3-over 74 that left him in a tie for seventh, four shots behind Reed and on the wrong side of the Hazeltine bubble.
As noted, the Top 100 advance to the next playoff event, and there still will be a 36-hole cut: Only the top 70 players plus ties will advance after Saturday's second round at the TPC Boston course in Norton.
Love will announce three of his four Ryder Cup captain s picks September 12 and save his fourth and final pick for September 25th. That moved him all the way up to No. 15, assuring two more playoff events and giving O'Hair a good shot at staying in the top 30 who qualify for the finale at the Tour Championship. He missed an 8-footer for par to suffer his first bogey in 55 holes.
Reed had gone 55 tournaments worldwide since starting 2015 with a victory at the Hyundai Tournament of Champions. Reed holed a 12-foot birdie putt on the next hole for a two-shot lead, and Fowler never got any closer.
The top 70 after next week advance to the third playoff event, with the top 30 going to East Lake for the Tour Championship.
The 20-year-old shot a 6-under 66 to beat Sei Young Kim (65) of South Korea by four strokes.
Fowler was on that 2014 US team, too. So playing the back nine all week. American David Lipsky (67) and Spain's Adrian Otaegui (67) were two strokes back.