Steve Stricker’s swing, for the first 68 holes of the Memorial Tournament, appeared completely devoid of tension, producing birdies so regularly that by the time players headed for cover at Muirfield Village Golf Club — about to endure a 21 / 2-hour weather delay — there seemed little reason to even return to the course. Stricker led by four shots much of Sunday, an advantage that seemed impenetrable.

Yet by the time long shadows fell across the course, there was Stricker, walking off the 18th green, smiling sheepishly as he shook hands with Jack Nicklaus, the tournament host. “It wasn’t pretty,” he said.

That it was not. But his victory thrusts Stricker into an interesting position. His closing 68 left him at 16 under par for the tournament, a shot better than Matt Kuchar and Brandt Jobe. It included a pair of clutch, par-saving putts at 16 and 17, when he made two of the better sand saves of his career. It will make him, when the world golf rankings are released Monday, the top American player in the world at fourth.

But will it make him better prepared to contend for his first major title at the U.S. Open, which begins June 16 at Bethesda’s Congressional Country Club?

“I don’t know why he hasn’t won a major yet,” Nicklaus said. “But as long as he wants to play, the next couple, three years — or even this year, the way he’s playing — watch out at Congressional.”

Stricker, 44, held on here not because he played wonderfully coming in, but because he dominated going out. His scores on Muirfield’s first nine the last three days: 30, 31 and 30. But somehow, he was 4 over for the week on the back. One reason: During and after the weather delay — which came when he was in the 13th fairway, with a three-shot lead — thoughts of impending doom entered his brain.

“The thought of blowing it and not performing down the stretch to win, it came through my mind,” Stricker said,

His best shots Sunday came when he looked to be in the most trouble. He made a gutsy play from a bunker at 12 — intending to land the ball in the fringe to slow its trickle to the hole, and pulling it off — to save par. At the murderous par-3 16th, when his lead was down to two, he flew his tee shot to the back bunker, then buried a 16-footer for another par save. His approach at 17 found yet another bunker, and he blasted to seven feet. “That putt was probably the tournament,” he said, and he made it.

Stricker now has 10 PGA Tour victories. He is ranked higher than Tiger Woods and Phil Mickelson. What he needs: a major.

“It’s always been a big goal, probably more so now than a few years ago,” Stricker said. “I feel like I’ve done a lot of nice things in my career, especially the last five or six years, that that would really top off my career.”

Stricker’s best finish in 15 Opens was fifth in 1999 at Pinehurst. He entered the final nine in 2007 at Oakmont right at the lead, and made double bogeys 10 and 11. Perhaps his best chance at a major came at the 1998 PGA Championship, in which he entered the final round tied for the lead with Vijay Singh. He shot 70. Singh shot 68 to win by two.

“The window of opportunity is probably getting smaller and smaller each and every time I play in a major,” Stricker said. “. . . So yeah, you could say it’s a little bit more on my mind.”

Just getting in is still on the minds of hundreds of golfers around the country, including several in the Memorial field. Eleven 36-hole sectional qualifying tournaments will be held Monday, including one in Columbus. Gary Woodland, a monstrous hitter who won in Tampa earlier in the season, is entered in that event.

But Woodland closed the Memorial with a 68 to finish in sixth despite a balky back. He entered this week ranked 54th in the world — and sixth will move him into the top 50. If he remains there after next week’s tournament, he gains entry into the Open field. So he left Muirfield on Sunday evening with a question: Play in the qualifier, or not?

“See what I’m ranked in the world tonight,” Woodland said. “We’ll go from there.”

Stricker was already comfortably in the field. Now, he will take a week off, then head to Congressional next Sunday. He’ll play nine-hole practice rounds for four straight days, and then tee it up for the 51st major of his career, carried by the confidence that he hung on here.