Day, who triumphed by six shots last year when the tournament was held at Plainfield Country Club, returned a 68.
"It was a clean day," Reed, a four-times winner on the PGA Tour, told reporters after a bogey-free round that also included an eagle and three birdies, all of them coming on his homeward nine. "I feel like I hit the ball pretty solid.
"All the shots I hit, even though (they) might not have been down some of the lines I wanted to, I was still in the fairway and still on the greens, so I was still able to attack."
Reed is scrambling for one of the last three automatic spots on the United States Ryder Cup team to take on holders Europe at Hazeltine outside Minneapolis from Sept. 30-Oct. 2.
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U.S. Open champion Dustin Johnson, Jordan Spieth, Phil Mickelson, PGA Championship winner Jimmy Walker and Ryder rookie Brooks Koepka have already secured their berths, with the final three automatic selections to be decided after The Barclays.
Reed, who sits eighth in the Cup standings, is vying with players such as Brandt Snedeker, Zach Johnson, Bubba Watson and Olympic bronze medallist Matt Kuchar for those spots.
"Of course it's on my mind," Reed said of his Cup bid. "But really at the end the day, it's just trying to get better and play this tournament. If I play well, that means those other guys are going to have to play even better to try to catch me."
Day, the game's hottest player over the past year with seven tournament wins in his last 23 starts, was relatively happy with a return of four birdies and a lone bogey in his first competitive round in nearly a month.
"Overall, I felt great about how I felt like I played," said the 28-year-old Australian, who finished second at the PGA Championship last month in his most recent start.
"Did a lot of good quality things out there, and hopefully I can just keep pushing that from the second to fourth round now."
American world number two Dustin Johnson opened with a 70 while Rio golf gold medallist Justin Rose, of England, battled to a 73.
Third-ranked American Jordan Spieth and fifth-ranked Northern Irishman Rory McIlroy were among the late starters on Thursday.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Andrew Both)
