JERSEY CITY, N.J.

Of all the players who missed putts on the 18th hole at Liberty National, Adam Scott might have been the only one who felt like it didn’t matter.

His 15-foot putt grazed the right edge of the cup, and Scott walked away with a 5- under 66 that he considered little more than a good final round.

More than an hour later, it turned out to be a winner at The Barclays.

“I can’t believe it, to be honest,” Scott said after opening the FedEx Cup playoffs with a one-shot win. “I just played a good round today and I came in and really didn’t think it had a chance. But obviously, things went my way a lot out there.

“I feel like I’ve been given a bit of a gift,” he said, “but I’ll take it.”

Even if Scott had made his birdie putt on the 18th, he figured he would be lucky to get into a playoff.

What followed was a parade of missed putts, ugly shots and Tiger Woods dropping to his knees just before he started dropping birdies.

“It was a good charge, but obviously I got a lot of luck, the guys struggled coming in,” Scott said. “I’ve been in their position, too. It’s hard getting it done and I was playing from a position of nothing to lose today.”

Justin Rose had a 25-foot birdie putt to take the outright lead, gunned it 5 feet by the hole, and missed the par putt to fall one shot behind. Kevin Chappell, whose birdie on the 10th hole gave him a two-shot lead, played the next seven holes in 7-over par, starting with a three-putt from 8 feet for double bogey.

Woods had been battling lower back issues all week, which he attributed to a soft bed in his hotel room. In a snapshot of the collapses that unfolded over the last two hours, Woods said he had a back spasm on the par-5 13th hole, and after his second shot with a fairway metal was so far left that it went into a water hazard on the other side of the 15th fairway, he dropped to all fours in pain and took his time getting back on his feet.

Woods at least made it interesting, as he often does. He birdied the 16th. He birdied the 17th to get within one shot. He had a 25-foot putt off the back of the 18th green to catch Scott, and it looked good all the way until stopping one turn short. Woods turned away in disbelief, the second time he has come up one shot short at Liberty National.

That last hope came from Gary Woodland, who chose driver off the 13th tee and hit it through the fairway and into the water, leading to bogey. Woodland never caught up, missing birdie putts inside 10 feet on his last three holes.

Rose, unlike Scott, knew exactly what his putt meant and wanted to be sure he gave it a good run.

“I got too aggressive,” said Rose, who closed with a 68. “I thought it was a putt to win the tournament. It’s tough to take.”

Woods put up a good fight despite looking to be uncomfortable over the final hour.

He was one shot behind going to the 12th hole when he felt a twinge in his lower back, which turned into a spasm on the 13th.

“I felt great until that tee shot at 12,” Woods told CBS Sports, later declining all over interview requests. “I was perfectly fine. I was playing pretty good, and I was hanging right there … and I was only one back. So I figured I was in the perfect spot, and unfortunately just couldn’t finish off the rest of the day.”

Woods closed with a 69, the first time in a year on the PGA Tour that he posted all four rounds in the 60s.

He left some doubt whether he would compete at the next playoff event, the Deutsche Bank Championship, which starts Friday on the TPC Boston.

“That’s all hypothetical right now,” Woods said. “I just got off and I’m not feeling my best right now.”

Only the top 100 players in the FedEx Cup advance to the second playoff event next week outside Boston. Geoff Ogilvy could have joined them except for missing a 2 1/2-foot par putt on the final hole that ultimately knocked him out of the top 100.