CARMEL, Ind. —Powerful off the tee and relentless with the putter, Dustin Johnson didn’t give anyone much of a chance Sunday by closing with a 5-under-par 67 to win the BMW Championship by three shots and move to the top of the FedEx Cup.

Johnson won for the third time in his last eight tournaments dating to his first major at the US Open, and this might have been his most complete performance.

‘‘I’ve got a lot of confidence in every part of my game,’’ Johnson said.

Paul Casey did just about everything he could, including two early birdies for two-shot swings that erased a four-shot deficit in two holes. Johnson answered with a pair of birdies and he was on his way. Casey made a 25-foot eagle putt on the 15th hole to get within one shot, but that lasted only as long as it took Johnson to make an 18-foot eagle putt on top of him to keep the margin at three shots.

Casey was runner-up in his second straight FedEx Cup playoff event, losing to Rory McIlroy a week ago. His consolation, along with $1,836,000 in those weeks, was the No. 5 seed at the Tour Championship in two weeks. That means he only has to win at East Lake to capture the $10 million bonus.

Rickie Fowler won’t have any chance at all.

Fowler, who started the week at No. 22 in the FedEx Cup, closed with a 71 and finished 59th at Crooked Stick. He was bumped out of the top 10 by the smallest margin in the 10-year history of the FedEx Cup — 0.57 points behind Charl Schwartzel, who closed with a 64.

The timing is particularly bad for Fowler because Davis Love III makes three of his captain’s picks for the Ryder Cup on Monday, with another one right after the Tour Championship. Fowler won’t have another chance to audition, though he might get picked Monday, anyway.

Asked if he had done enough to be picked, Fowler said, ‘‘I would like to think so.’’

‘‘I’ve done basically everything I can do as far as schedule and playing,’’ said Fowler, who left the Olympics to play the following week on the PGA Tour. ‘‘It would have been nice to play better to make the pick a lot easier on him.’’

J.B. Holmes tied for fourth, key for him because the big hitter from Kentucky also needs a captain’s pick to play in the Ryder Cup.

“I feel like I played well enough to get that shot,’’ Holmes said. ‘‘We’ll see.’’

Roberto Castro holed out for eagle from the seventh fairway on his way to a 67 to finish alone in third, sending the Georgia Tech grad and Atlanta resident home to play in the Tour Championship for the second time.

All this activity was far more compelling than the actual tournament, for Johnson never looked as though he was going to lose — no matter how well Casey played. Johnson already has introduced a fade to his powerful driving. He dialed in his wedges earlier this year, and is now among the best. And he changed to a different putter this week to help him start the ball on line, and it worked magnificently.

Johnson is regarded as golf’s greatest athlete, and to see every part of his game in order is a daunting sight. He played the par 5s in 15 under for the week.

Matt Kuchar closed with a 71 and tied for fourth, along with Ryan Palmer (70), Adam Scott (71), Schwartzel and Holmes. Palmer had a chance to get into the top 30 except for missing a 12-foot par putt on the 16th hole and a 15-foot birdie putt on the final hole.

Fowler wasn’t the only player to drop out of the top 30. Sergio Garcia shot 73 and dropped from No. 25 to No. 32. Henrik Stenson also fell out of the top 30. He was at No. 24 and chose not to play this week to rest his knee for the Ryder Cup.

Jason Day, who entered as the world’s No. 1 player, withdrew after eight holes with back pain, making him ineligible for the Vardon Trophy.

Day has a history of back issues, most recently at the Dell Match Play in the spring. He barely made it through the opening round when his back locked up on him prompting him to consider pulling out. The back got better, and Day went on to win.

He was 2-over par for his final round at Crooked Stick and in the middle of the pack when his agent, Bud Martin, said he felt pain stooping to pick up his tee.

The injury was not considered serious, and Day was hopeful of being in Atlanta in two weeks for the Tour Championship and a shot at the $10 million FedEx Cup bonus.

The Australian was leading the Vardon Trophy for the lowest adjusted scoring average going into the BMW Championship.

However, players who withdraw in the middle of a round are not eligible for the award from the PGA of America, which dates to 1937.

Day went straight for treatment.

‘‘I don’t think it’s anything he hasn’t dealt with before,’’ Martin said. ‘‘He just bent over and it kind of went on him on the ninth hole. Instead of forcing it, we just decided that it was more prudent to come in, get it worked on and deal with it.’’

Martin said Day might choose to have more tests next week just to be sure, but ‘‘my gut is that he’ll be fine.’’

The PGA Tour is off next week. The Tour Championship for the top 30 players starts Sept. 22 at East Lake.

‘‘Hopefully, he’ll be ready for Atlanta,’’ Martin said. ‘‘But the most important thing is the next 15 years, not the next 15 days.’’